Abstract
Papers on braid theory and some of its generalization and applications, reviewed in Referativnyi Zhurnal “Matematika” during 1953–1977, as well as individual papers on an earlier period, are surveyed.
Similar content being viewed by others
Literature cited
V. I. Arnol'd, “A remark on the branching of hyperelliptic integrals as functions of the parameters,” Funkts. Analiz Ego Prilozhen.,2, No. 3, 1–3 (1968).
V. I. Arnol'd, “On the braids of algebraic functions and the cohomologies of swallowtails,” Usp. Mat. Nauk,23, No. 4, 247–248 (1968).
V. I. Arnol'd, “Cohomology ring of the group of dyed braids,” Mat. Zametki,5, No. 2, 227–231 (1969).
V. I. Arnol'd. “On cohomology classes of algebraic functions preserved under Tschirnhausen transformations,” Funkts. Analiz Ego Prilozhen.,4, No. 1, 84–85 (1970).
V. I. Arnol'd, “On certain topological invariants of algebraic functions,” Tr. Mosk. Obshch.,21, 27–46 (1970).
V. I. Arnol'd, “Topological invariants of algebraic functions. II,” Funkts. Analiz Ego Prilozhen.,4, No. 2, 1–9 (1970).
V. I. Arnol'd, “Normal forms of functions close to degenerate critical points, Weyl groups Ak. Dk. Ek. and Lagrange singularities,” Funkts. Analiz Ego Prilozhen.,6, No. 4, 3–25 (1972).
V. I. Arnol'd, “Critical points of functions and classification of caustics,” Usp. Mat. Nauk,29, No. 3, 243–244 (1974).
V. I. Arnol'd, “Critical points of smooth functions and their normal forms,” Usp. Mat. Nauk,30, No. 5, 3–65 (1975).
V. I. Arnol'd, “Critical points of functions on a manifold with boundary, simple Lie groups Bk. Ck. F4. and singularities of evolutes,” Usp. Mat. Nauk,33, No. 5, 91–105 (1978).
N. Bourbaki, Éléments de Mathématique. Fase. XXXIV. Groupes et Algèbres de Lie. Chapitre IV: Groupes de Coxeter et Systèmes de Tits. Chapitre V: Groupes Engendrés par des Réflexions. Chapitre VI: Systèmes de Racines. Hermann et Cie., Paris (1968).
N. M. Vainberg, “On the free equivalence of closed braids,” Dokl. Akad. Nauk SSSR,23, 215–216 (1939).
P. V. Vainshtein, “Cohomologies of braid groups,” Funkts. Analiz Ego Prilozhen.,12, No. 2, 72–73 (1978).
A. N. Varchenko, “On the branching of multiple integrals depending on parameters,” Funkts. Analiz Ego Prilozhen.,3, No. 4, 79–80 (1969).
É. B. Vinberg and O. V. Shvartsman, “Riemann surfaces,” in: Algebra. Topology. Geometry [in Russian], Vol. 16, Itogi Nauki i Tekh., VINITI Akad. Nauk SSSR, Moscow (1978), pp. 191–245.
O. Ya. Viro, “Links, two-sheeted branching coverings, and braids,” Mat. Sb.,87, No. 2, 216–228 (1972).
E. A. Gorin, “On the factorization of abstract entire functions,” Usp. Mat. Nauk,25, No. 4, 177–178 (1970).
E. A. Gorin, “Equations with abstract entire functions in Banach algebras,” in: Materials of Eighth Math. Interinst. Sci. Conf. Far East [in Russian], Khabarovsk (1970), pp. 9–12.
E. A. Gorin, “Several examples connected with algebraic equations in algebras of functions,” Dokl. Akad. Nauk SSSR,200, No. 2, 273–276 (1971).
E. A. Gorin, “On certain algebraic equations with holomorphic coefficients,” Usp. Mat. Nauk,27, No. 3, 197–198 (1972).
E. A. Gorin, “On algebraic equations in algebras of continuous functions,” Rept. Abstr. Sixth All-Union Topol. Conf. [in Russian], Metsniereba, Tbilisi (1972), p. 43.
E. A. Gorin, “Holomorphic functions on an algebraic manifold and the reducibility of separable polynomials over certain commutative Banach Algebras,” Rept, Abstr. Seventh All-Union Topol. Conf. [in Russian], Minsk (1977), p. 55.
E. A. Gorin, “Algebraic equations in commutative Banach algebras and related questions,” Zap. Nauchn. Sem. LOMI Akad. Nauk SSSR,81, 58–61 (1978).
E. A. Gorin, “On the researches of G. E. Shilov on the theory of commutative Banach algebras and their subsequent development, Usp. Mat. Nauk,33, No. 4, 169–189 (1978).
E. A. Gorin and V. Ya. Lin, “Algebraic equatons with continuous coefficients, “Material Seventh Math. and Seventh. Phys. Interinst. Sci. Conf. Far East [in Russian], Khabarovsk (1968), pp. 10–12.
E. A. Gorin and V. Ya. Lin, “Braid groups and algebraic equations with continuous coefficients, “Usp. Mat. Nauk,24, No. 2, 225–226 (L969).
E. A. Gorin and V. Ya. Lin, “Algebraic equations with continuous coefficients and certain questions in the algebraic theory of braids,” Mat. Sb.,78, No. 4, 579–610 (1969).
E. A. Gorin and V. Ya. Lin, “On separable polynomials over commutative Banach algebras,” Dokl. Akad. Nauk SSSR,218, No. 3, 505–508 (1974).
E. A. Gorin and C. Sánchez-Fernández, “On transcendental equations in commutative Banach algegras,” Funkt. Analiz. Ego, Prilozhen.,11, No. 1, 63–64 (1977).
V. V. Goryunov, “Cohomologies of braid groups of series C and D and certain stratifications,” Funkt. Analiz. Ego Prilozhen.,12, No. 2, 76–77 (1978).
S. Zdravkovska, “Topological classification of polynomial mappings,” Usp. Mat. Nauk,25, No. 4 179–180 (1970).
V. M. Zinde, “Commutator subgroups of Artin groups,” Usp. Mat. Nauk,30, No. 5, 207–208 (1975).
V. M. Zinde, “Certain homomorphisms of Artin groups of series Bn and Dn into groups of the same series and into symmetric groups,” Usp. Mat. Nauk,32, No. 1, 189–190 (1977).
V. M. Zinde, “Analytic properties of spaces of regular orbits of Coxeter groups of serie B and D, “Funkts. Analiz Ego Prilozhen.,11, No. 1, 69–70 (1977).
V. M. Zinde, “Homomorphisms of Artin groups of series B and D,” Moscow Univ., Moscow (1977) (Manuscript deposited in VINITI, June 6, 1977, No. 2230-77 Dep.).
V. M. Zinde, “Holomorphic mappings of spaces of regular orbits of Coxeter groups of series B and D,” Sib. Mat. Zh.,18, No. 5, 1015–1026 (1977).
Yu. V. Zyuzin, “Algebraic equations with continuous coefficients on uniform spaces,” Vestn. Mosk. Univ., No. 1, 51–53 (1972).
Yu. V. Zyuzin, “Irreducible holomorphic separable polynomials on bouquets of circular annuli,” Usp. Mat. Nauk,29, No. 5, 221–222 (1974).
Yu. V. Zyuzin, “Irreducible separable polynomials with holomorphic coefficients on a certain class of complex spaces,” Mat. Sb.,102, No. 4, 569–591 (1977).
Yu. V. Zyuzin, “Separable polynomials over functional algebras,” Author's abstract of dissertation for the academic degree of Candidate of Phys.-Math. Sciences, Mosk. Gos. Univ., Moscow (1974).
Yu. V. Zyuzin and V-Ya. Lin, “Nonbranching algebraic extensions of commutative Banach algebras,” Mat. Sb.,91, No. 3, 402–420 (1973).
Sh. I. Kaliman, “Holomorphic universal covering of the space of polynomials without multiple roots,” Funkts. Analiz Ego Prilozhen.,9, No. 1, 71 (1975).
Sh. I. Kaliman, “Holomorphic endomorphisms of the manifold of complex polynomials with, discriminant 1,” Usp. Mat. Nauk,31, No. 1, 251–252 (1976).
Sh. I. Kaliman, “Holomorphic universal covering of the space of polynomials without multiple roots,” Teoriya Funktsii, Funkt, Analiz. Ikh Prilozhen., Resp, Nauchn, Sb., No. 28, 25–35 (1977).
Sh. I. Kaliman, “Holomorphic endomorphisms of complex Weyl chambers of series Dn.” Usp. Mat. Nauk,34, No. 2, 201–202 (1979).
F. Klein, Vorlesungen über Höhere Geometrie, Dritte Auflage, Verlag von Julius Springer, Berlin (1926).
A. G. Kurosh; Theory of Groups [in Russian.], 3rd aug, ed., Nauka, Moscow (1967).
V. Ya. Lin, “Algebroid functions and holomorphic elements of homotopy groups of a complex manifold,” Dokl. Akad. Nauk SSSR,201, No. 1, 28–31 (1971).
V. Ya. Lin, “On the representations of a braid group by permutations,” Usp. Mat. Nauk.27, No. 3, 192 (1972).
V. Ya. Lin, “Algebraic functions with a universal discriminant manifold,” Funkt, Analiz Ego Prilozhen.,6, No. 1, 81–82 (1972).
V. Ya. Lin, “On the superpositions of algebraic functions,” Funkts. Analiz. Ego Prilozhen.,6, No. 3, 77–78 (1972).
V. Ya. Lin, “Representations of braids by permutations,” Usp. Mat. Nauk,29, No. 1, 173–174 (1974).
V. Ya. Lin, “On fourth-degree polynomials over the algebra of continuous functions,” Funkts. Analiz Ego Prilozhen.,8, No. 4, 89–90 (1974).
V. Ya. Lin, “Superpositions of algebraic functions,” Funkts. Analiz Ego Prilozhen.,10, No. 1, 37–45 (1976).
V. Ya. Lin, “Holomorphic mappings of certain spaces connected with algebraic functions,” Zap. Nauchn. Sem. LOMI Akad. Nauk SSSR,81, 62–65 (1978).
O. V. Lyashko, “Geometry of bifurcation diagrams,” Usp. Mat. Nauk,34, No. 3, 205–206 (1979).
W. Magnus, A. Karrass, and D. Solitar, Combinatorial Group Theory: Presentations of Groups in Terms of Generators and Relations, Interscience Publishers, New York (1966).
G. S. Makanin, “The conjugacy problem in a braid group,” Dokl. Akad. Nauk SSSR,182, No. 3, 495–496 (1968).
G. S. Makanin, “On the normalizers of a braid group,” Mat. Sb.,86, No. 2, 171–179 (1971).
A. I. Mal'tsev, “On an isomorphic representation of infinite groups of matrices,” Mat. Sb.,4, 405–422 (1940).
A. A. Markov, “Über die freie Äquivalenz der geschlossener Zöpfe,” Mat. Sb.,1, 73–78 (1936).
A. A. Markov, Foundations of the Algebraic Theory of Tresses, Tr. Mat. Inst. Steklov, Vol. 16, Moscow (1945).
H. Neumann, Varieties of Groups, Springer-Verlag, Berlin-Heidelberg-New York (1967).
B. I. Plotkin, Automorphism Groups of Algebraic Systems [in Russian], Nauka, Moscow (1966).
D. M. Smirnov, “On the theory of residually finite groups,” Ukr. Mat. Zh.,15, No. 4, 453–457 (1963).
V. B. Styshnev, “Extraction of a root in a braid group,” Izv. Akad. Nauk SSSR, Ser. Mat.,42, No. 5, 1120–1131 (1978).
D. B. Fuks, “Cohomologies of a braid group mod 2,” Funkts. Analiz Ego Prilozhen.,4, No. 2, 62–73 (1970).
D. B. Fuks, “Quillenization and Bordism,” Funkts. Analiz Ego Prilozhen.,8, No. 1, 36–42 (1974).
M. Hall, The Theory of Groups, MacMillan Co., New York (1959).
S. I. Epshtein, “Fundamental groups of spaces of collections of relatively prime polynomials,” Funkts. Analiz Ego Prilozhen.,7, No. 1, 90–91 (1973).
J. W. Alexander, “A lemma on systems of knotted curves,” Proc. Nat. Acad. Sci. U.S.A.,9, 93–95 (1923).
E. Artin, “Theorie der Zöpfe,” Abh. Math. Sem. Univ. Hamburg,4, 47–72 (1925).
E. Artin, “Theory of Braids,” Ann. Math.,48, No. 1, 101–126 (1947).
E. Artin, “Braids and permutations,” Ann. Math.,48, No. 3, 643–649 (1947).
E. Artin, “The theory of braids,” Am. Sci.,38, 112–119 (1950).
R. Baer, “Über Kurventypen auf Flächen,” J. Reine Angew. Math.,156, 231–246 (1927).
R. Baer, “Die Abbildungstypen-Gruppe der orientierbaren geschlossen Flaeche vom Geschlechte 2,” J. Reine Angew. Math.,160, 1–25 (1929).
G. Baumslag, “Automorphism groups of residually finite groups,” J. London Math. Soc.,38, No. 1, 117–118 (1963).
J. S. Birman, “Braid groups and their relationship to mapping class groups,” Doctoral Dissertation, New York Univ., New York (1968).
J. S. Birman, “On braid groups,” Commun. Pure Appl. Math.,22, No. 1, 41–72 (1969).
J. S. Birman, “Mapping class groups and their relationship to braid groups,” Commun. Pure Appl. Math.,22, No. 2, 213–238 (1969).
J. S. Birman, “Nonconjugate braids can define isotopic knots,” Commun. Pure Appl. Math.,22, No. 2, 239–242 (1969).
J. S. Birman, “Automorphisms of the fundamental group of a closed, orientable 2-manifold,” Proc. Am. Math. Soc.,21, No. 2, 351–354 (1969).
J. S. Birman, “Abelian quotients of the mapping class group of a 2-manifold,” Bull. Am. Math., Soc.,76, No. 1, 147–150 (1970).
J. S. Birman, “A normal form in the homeotopy group of a surface of genus 2, with applications to 3-manifolds,” Proc. Am. Math. Soc.,34, No. 2, 379–384 (1972).
J. S. Birman, “Plat representations for link groups,” Commun. Pure Appl. Math.,26, No. 5–6, 673–678 (1973).
J. S. Birman, “Mapping class groups of surfaces: a survey,” in: L. Greenberg (ed.), Discontinuous Groups and Riemann Surfaces, Ann. Math. Studies, No. 79, Princeton Univ. Press, Princeton, NJ (1974), pp. 57–71.
J. S. Birman, “Poincare's conjecture and the homeotopy group of a closed, orientable 2-manifold,” J. Austral. Math. Soc.,17, No. 2, 214–221 (1974).
J. S. Birman, Braids, Links, and Mapping Class Groups, Ann. Math. Studies, No. 82, Princeton Univ. Press, Princeton, NJ (1975).
J. S. Birman, “On the stable equivalence of plat representations of knots and links,” Can. J. Math.,28, No. 2, 264–290 (1976).
J. S. Birman and D. R. J. Chillingworth, “On the homeotopy group of a nonorientable surface,” Proc. Cambridge Philos. Soc.,71, No. 3, 437–438 (1972).
J. S. Birman and H. M. Hilden, “On the mapping class groups of closed surfaces and as covering spaces,” in: L. V. Ahlfors, L. Bers, H. M. Farkas, R. C. Gunning, I. Kra, and H. E. Rauch (eds.), Advances in the Theory of Riemann Surfaces, Ann. Math. Studies, No. 66, Princeton Univ. Press, Princeton, NJ (1971), pp. 81–115.
J. S. Birman and H. M. Hilden, “Lifting and projecting homeomorphisms,” Arch. Math.,23, No. 4, 428–434 (1972).
J. S. Birman and H. M. Hilden, “Isotopies of homeomorphisms of Riemann surfaces and a theorem about Artin's braid group,” Bull. Am. Math. Soc.,78, No. 6, 1002–1004 (1972).
J. S. Birman and H. M. Hilden, “On isotopies of homeomorphisms of Riemann surfaces,” Ann. Math.,97, No. 3, 424–439 (1973).
J. S. Birman and H. M. Hilden, “The homeomorphism problem for S3” Bull. Am. Math. Soc.,79, No. 5, 1006–1009 (1973).
J. S. Birman and H. H. Hilden, “Heegaard splittings of branched coverings of S3.” Trans. Am. Math. Soc.,213, 315–352 (1975).
J. S. Birman and W. Magnus, “Discriminant and projective invariants of binary forms,” Commun. Pure Appl. Math.,23, No. 3, 269–275 (1970).
F. Bohnenblust, “The algebraic braid group,” Ann. Math.,48, No. 1, 127–136 (1947).
E. Brieskorn, “Sur les groupes de tresses [d'après V. I. Arnol'd],” in: Séminaire Bourbaki, Vol. 1971/72, Exposés 400-417, Lect. Notes Math., Vol. 317, Springer-Verlag, Berlin-Heidelberg-New York (1973), pp. 21–44.
E. Brieskorn, “Die fundamentalgruppe des Raumes der regulären Orbits einer endlichen komplexen Spiegelungsgruppe,” Invent. Math.,12, No. 1, 57–61 (1971).
E. Brieskorn and K. Saito, “Artin-Gruppen und Coxeter-Gruppen,” Invent. Math.,17, No. 4, 245–271 (1972).
W. Burau, “Über Zopfinvarianten,” Abh. Math. Sem. Univ. Hamburg,9, 117–124 (1932).
W. Burau, “Über Zopfgruppen und gleichsinning verdrillte Verkettungen,” Abh. Math. Sem. Univ. Hamburg,11, 179–186 (1935).
W. Burau, “Über Verkettungsgruppen,” Abh. Math. Sem. Univ. Hamburg,11, 171–178 (1935).
G. Burde, “Zur Theorie der Zöpfe,” Math. Ann.,151, No. 2, 101–107 (1963).
G. Burde, “Über Normalisatoren der Zopfgruppen,” Abh. Math. Sem. Univ. Hamburg,27, No. 1–2, 97–115 (1964).
G. Burde and K. Murasugi, “Links and Seifert fiber spaces,” Duke Math. J.,37, No. 1, 89–93 (1970).
W.-L. Chow, “On the algebraic braid group,” Ann. Math.,49, No. 3, 654–658 (1948).
D. B. Cohen, “The Hurwitz monodromy group,” J. Algebra,32, No. 3, 501–517 (1974).
D. I. A. Cohen, “On representations of the braid group,” J. Algebra,7, No. 2, 145–151 (1967).
F. R. Cohen, “Braid orientations and bundles with flat connections,” Invent. Math.,46, No. 2, 99–110 (1978).
F. R. Cohen, T. J. Lada, and J. P. May, The Homology of Iterated Loop Spaces, Lect. Notes Math., Vol. 533, Springer-Verlag, Berlin-Heidelberg-New York (1976).
T. M. Cowan, “The theory of braids and the analysis of impossible figures,” J. Math. Psychol.,11, No. 3, 190–212 (1974).
D. M. Dahm, “A generalization of braid theory,” Doctoral Dissertation, Princeton Univ., Princeton, NJ (1962).
M. Dehn, “Die Gruppe der Abbildungsklassen,” Acta Math.,69, 135–206 (1838).
P. Deligne, “Les immeubles des groupes de tresses généralisés,” Invent. Math.,17, No. 4, 273–302 (1972).
E. Dyer and R. K. Lashof,” Homology of iterated loop spaces,” Am. J. Math.,84, No, 1, 35–88 (1962).
M. Engber, “A strengthening of centerlessness in Teichmüller theory,” Proc. Am. Math. Soc.,60, 144–148 (1976).
E. Fadell, “Homotopy groups of configuration spaces and the string problem of Dirac,” Duke Math. J.,9, No. 2, 231–242 (1962).
E. Fadell and L. Neuwirth, “Configuration spaces,” Math. Scand.,10, No. 1, 111–118 (1962).
E. Fadell and J. Van Buskirk, “On the braid groups of E2 and S2.” Bull. Am. Math. Soc.,67, No. 2, 211–213 (1961).
E. Fadell and J. Van Buskirk, “The braid groups of E2 and S2.” Duke Math. J.,29, No. 2, 243–257 (1962).
R. H. Fox and L. Neuwirth, “The braid groups,” Math. Scand.,10, No. 1, 119–126 (1962).
R. Fricke and E. Klein, Vorlesungen über die Theorie der automorphen Funktionen. Band I: Die Gruppentheoretischen Grundlagen. Teubner, Stuttgart (1897); Johnson Reprint Corp., New York (1965).
W. Fröhlich, “Über ein spezielles Transformationsproblem bei einer besonderen Klasse von Zöpfen,” Monatsh. Math. Phys.,44, 225–237 (1936).
F. A. Garside, “The theory of knots and associated problems,” Doctoral Dissertation, Oxford Univ., Oxford (1965).
F. A. Garside, “The braid group and other groups,” Q. J. Math.,20, No. 78, 235–254 (1969).
B. J. Gassner, “On braid groups,” Abh. Math. Sem. Univ. Hamburg,25, No. 1–2, 10–22 (1961).
R. Gillette and J. Van Buskirk, “The word problem and consequences for the braid groups and mapping class groups of the 2-sphere,” Trans. Am. Math. Soc.,131, No. 2, 277–296 (1968).
J. Gilman, “An example about normalizers in mapping class groups,” Proc. Am. Math. Soc.,69, No. 1, 115–118 (1978).
C. H. Goldberg, “An exact sequence of braid groups,” Math. Scand.,33, No. 1, 69–82 (1973).
D. L. Goldsmith, “Motions of links in the 3-sphere,” Doctoral Dissertation, Princeton Univ., Princeton, NJ (1972).
D. L. Goldsmith, “Homotopy of braids—in answer to a question of E. Artin,” in: R. F. Dickman, Jr. and P. Fletcher (eds.), Topology Conference, Lect. Notes Math., Vol. 375, Springer-Verlag, Berlin-Heidelberg-New York (1974), pp. 91–96.
D. L. Goldsmith, “Motions of links in the 3-sphere,” Bull. Am. Math. Soc.,80, No. 1, 62–66 (1974).
E. K. Grossman, “On the residual finiteness of certain mapping class groups,” J. London Math. Soc.,9, No. 1, 160–164 (1974).
E. K. Grossman, “On certain permutation representations of mapping class groups,” Math. Z.,146, No. 2, 105–112 (1976).
H. M. Hilden, “Generators for two groups related to the braid group,” Pacif. J. Math.,59, No. 2, 475–486 (1975).
A. Hurwitz, “Über Riemann'sche Flächen mit gegebenen Verzweigungspunkten,” Math. Ann.,39, 1–61 (1891).
T. Kaneto, “On isotopy groups of holed spheres,” Sci. Rep. Tokyo Kyoiku Daigaku, Sec. A, No. 347–365, 46–51 (1975).
T. Kaneto, “On isotopy groups of simply connected holed manifolds,” Sci. Rep. Tokyo Kyoiku Daigaku, Sec. A, No. 347–365, 52–58 (1975).
Y. Ladegaillerie, “Groupes de tresses et problème des mots dans les groupes de tresses,” Bull. Sci. Math.,100, No. 3, 255–267 (1976).
Y. Ladegaillerie, “Decoupes et isotopies de surfaces topologiques,” Thèse Doct. Sci. Math., Univ. Sci. et Techn. Langudoc, Langudoc (1976).
H. Levinson, “Decomposable braids,” Doctoral Dissertation, New York Univ., New York (1971).
H. Levinson, “Decomposable braids and linkages,” Trans. Am. Math. Soc.,178, 111–126 (1973).
H. Levinson, “Decomposable braids as subgroups of braid groups,” Trans. Am. Math. Soc.,202, 51–55 (1975).
A. Libgober, “On the fundamental group of the space of cubic surfaces,” Math. Z.,162, No. 1, 63–67 (1978).
W. B. R. Lickorish, “Homomorphisms of nonorientable two-manifolds,” Proc. Cambridge Philos. Soc.,59, No. 2, 307–317 (1963).
W. B. R. Lickorish, “A finite set of generators for the homeotopy group of a 2-manifold,” Proc. Cambridge Philos. Soc.,60, No. 4, 769–778 (1964).
W. B. R. Lickorish, “On the homeotopy group of a 2-manifold (corrigendum),” Proc. Cambridge Philos. Soc.,62, No. 4, 679–681 (1966).
S. Lipschutz, “On a finite matrix representation of the braid group,” Arch. Math.,12, No. 1, 7–12 (1961).
S. Lipschutz, “Ntate on a paper by Shepperd on the braid group,” Proc. Am. Math. Soc.,14, No. 2, 225–227 (1963).
E. Looijenga, “The complement of the bifurcation variety of a simple singularity,” Invent. Math.,23, No. 2, 105–116 (1974).
C. Maclachlan, “On a conjecture of Magnus on the Hurwitz monodromy group,” Math. Z.,132, No. 1, 45–50 (1973).
C. Maclachlan, “Note on the Hurwitz-Nielsen realization problem,” Proc. Am. Math. Soc.,64, No. 1, 87–90 (1977).
C. Maclachlan, “On representations of Artin's braid group,” Mich. Math. J.,25, No. 2, 235–244 (1978).
C. Maclachlan and W. J. Harvey, “On mapping-class groups and Teichmüller spaces,” Proc. London Math. Soc.,30, No. 4, 496–512 (1975).
W. Magnus, “Über Automorphismen von Fundamentalgruppen berandeter Flachen,” Math. Ann.,109, No. 5, 617–646 (1934).
W. Magnus,” Residually finite groups,” Bull. Am. Math. Soc.,75, No. 2, 305–316 (1969).
W. Magnus, “Braids and Riemann surfaces,” Commun. Pure Appl. Math.,25, No. 2, 151–161 (1972).
W. Magnus, “Braid groups: a survey,” in: M. F. Newman (ed.), The Theory of Groups, Lect. Notes Math., Vol. 372, Springer-Verlag, Berlin-Heidelberg-New York (1974), pp. 463–487.
W. Magnus, “Two generator subgroups of PSL(2,C),” Nachr. Akad. Wiss, Göttingen, Math. Phys. Kl., II, No. 7, 1–14 (1975).
W. Magnus and A. Peluso, On knot groups,” Commun. Pure Appl. Math.,20, No, 4, 749–770 (1967).
W. Magnus and A. Peluso, “On a theorem of V. I. Arnol'd,” Commun. Pure Appl. Math.,22, No. 5, 683–692 (1969).
W. Mangier, “Die Klassen von topologischen Abbildungen einer geschlossenen Flache auf sich,” Math. Z.,44, No. 4, 541–554 (1939).
G. S. McCarthy, Jr., “Homeotopy groups,” Trans. Am. Math. Soc.,106, No. 2, 293–304 (1963).
J. W. Milnor, “Link groups,” Ann. Math.,59, No. 2, 177–195 (1954).
J. W. Milnor, “Isotopy of links,” in: R. H. Fox, D. C. Spencer, and A. W. Tucker (eds.), Algebraic Geometry and Topology: A Symposium in Honor of S. Lefschetz, Princeton Univ. Press, Princeton, N. J. (1957), pp. 280–306.
K. Murasugi, On Closed 3-Braids, Mem. Am. Math. Soc., No. 151, Am. Math. Soc., Providence, RI (1974).
K. Murasagi, “On the divisibility of knot groups,” Pacif. J. Math.,52, No. 2, 491–503 (1974).
K. Murasugi, “Seifert fiber spaces and braid groups,” Preprint, Toronto (1979).
K. Murasugi and R. S. D. Thomas, “Isotppic closed nonconjugate braids,” Proc. Am. Math. Soc.,33, No. 1, 137–139 (1972).
M. H. A. Newman, “On a string problem of Dirac,” J. London Math. Soc.,17, No. 3, 173–177 (1942).
J. Nielsen,” Über topologische Abbildungen geschlossener Flächen,” Abh. Math. Sem. Univ. Hamburg,3, 246–260 (1924).
J. Nielsen, “Untersuchungen zur Topologie der geschlossenen zweiseitigen Flächen, I–III,” Acta Math.,50, 189–358 (1927);53, 1–76 (1929);58, 87–167 (1931).
J. Powell, “Two theorems on the mapping class group of a surface,” Proc. Am. Math. Soc.,68, No. 3, 347–350 (1978).
L. V. Quintas, “Solved and unsolved problems in the computation of homeotopy groups of 2-manifolds,” Trans. N. Y. Acad. Sci.,30, No. 7, 919–938 (1968).
G. P. Scott, “The space of homeomorphisms of a 2-manifold,” Topology,9, No. 1, 97–109 (1970).
G. P. Scott, “Braid groups and the group of homeomorphisms of a surface,” Proc. Cambridge Philos. Soc.,68, No. 3, 605–617 (1970).
G. B. Segal, “Configuration-spaces and iterated loop-spaces,” Invent. Math.,21, No. 3, 213–221 (1973).
J. A. H. Shepperd, “Braids which can be plaited with their threads tied together at each end,” Proc. R. Soc.,A265, No. 1321, 229–244 (1962).
N. Smythe, “Isotopy invariants of links,” Doctoral Dissertation, Princeton Univ., Princeton, NJ (1965).
D. J. Sprows, “Homeotopy groups of compact 2-manifolds,” Fund, Math.,90, No. 1, 99–103 (1975).
R. S. D. Thomas, “An algorithm for combing braids,” Proc. 2nd Louisiana Conf, Combinatorics, Graph Theory, and Computing, Baton Rouge, LA (1971), pp. 517–532.
R. S. D. Thomas, “Partially closed braids,” Can. Math. Bull.,17, No. 1, 99–107 (1974).
R. S. D. Thomas, “The structure of the fundamental braids,” Q. J. Math.,26, No. 103, 283–288 (1975).
R. S. D. Thomas and B. T. Paley, “Garside's braid-conjugacy solution implemented,” Util. Math.,6, 321–335 (1974).
J. Tits, “Le problème des mots dans les groupes de Coxeter,” Symposia Mathematica, Vol. I, Academic Press Inc. (London) Ltd., London-New York (1969), pp. 175–185.
J. Van Buskirk, “Braid groups of compact 2-manifolds with elements of finite order,” Trans. Am. Math. Soc.,122, No. 1, 81–97 (1966).
H. Zieschang, “On the homeotopy groups of surfaces,” Math. Ann.,206, No. 1, 1–21 (1973).
Additional information
Translated from Itogi Nauki i Tekhniki, Algebra, Topologiya, Geometriya, Vol. 17, pp. 159–227, 1979.
Rights and permissions
About this article
Cite this article
Lin, V.Y. Artin braids and the groups and spaces connected with them. J Math Sci 18, 736–788 (1982). https://doi.org/10.1007/BF01091963
Issue Date:
DOI: https://doi.org/10.1007/BF01091963