References
Adams, J.F.: A new proof of a theorem of W.H. Cockcroft. J. London Math. Soc.30, 482–488 (1955)
Beckmann, W.H.: Completely aspherical 2-complexes. Ph.d. thesis, Cornell 1980
Beckmann, W.H.: A certain class of non-aspherical 2-complexes. J. Pure Appl. Alg.16, 243–244 (1980)
Brandenburg, J., Dyer, M.N.: On the aspherical Whitehead conjecture. Preprint 1979
Brown, R.: On the second relative homotopy group of an adjunction space: and exposition of a theorem of J.H.C. Whitehead. J. London Math. Soc. (2)22, 146–152 (1980)
Brown, R., Higgins, P.J.: On the connection between the second relative homotopy groups of some related spaces. Proc. London Math. Soc. (3)36, 193–212 (1978)
Brown, R., Huebschmann, J.: Identities among relations. In: Low-dimensional topology, Proc. Bangor Symp. 1979. R. Brown, T.L. Thickstun, eds. London Math. Soc. Lecture Note Series, Cambridge University Press (1981) (to appear)
Buoncristiano, S., Rourke, C.P., Sanderson, B.J.: A geometric approach to homology theory. London Math. Soc. Lecture Note Series, Vol. 18. Cambridge Cambridge University Press 1976
Cockcroft, W.H.: Note on a theorem due to J.H.C. Whitehead. Quart. J. Math.2, 159–160 (1951)
Cockcroft, W.H.: On two-dimensional aspherical complexes. Proc. London Math. Soc. (3)4, 375–384 (1954)
Chiswell, I.M., Collins, D.J., Huebschmann, J.: Aspherical group presentations. Math. Z.178, 1–36 (1981)
Cohen, J.M.: Aspherical 2-complexes. J. Pure Appl. Alg.12, 101–110 (1978)
Collins, D.J., Huebschmann, J.: Spherical diagrams and identities among relations. Preprint 1981
Dunwoody, M.J.: Answer to a conjecture of J.M. Cohen, J. Pure Appl. Alg.16, 249 (1980)
Fenn, R.: Letter to P. Stefan (unpublished)
Gutierrez, M.A., Ratcliffe, J.G.: On the second homotopy group. Quart. J. Math. Oxford (2)32, 45–55 (1081)
Hempel, J.: 3-manifolds, Annals of Mathematics Studies, Vol. 86. Princeton: Princeton University Press 1976
Hilton, P.J.: An Introduction to homotopy theory. Cambridge: Cambridge University Press 1953
Howie, J.: Aspherical and acyclic 2-complexes. J. London Math. Soc. (2)20, 549–558 (1979)
Igusa, K.: The generalized Grassmann invariantK 3(ℤ[π])→H 0(π,ℤ2[π]) (preprint)
Lyndon, R.C.: Cohomology theory of groups with a single defining relation. Ann. Math.52, 650–665 (1950)
Lyndon, R.C.: Dependence and independence in free groups. J. Reine Angew. Math.210, 148–174 (1962)
Lyndon, R.C.: On the Freiheitssatz. J. London Math. Soc. (2)5, 95–101 (1972)
Lyndon, R.C., Schupp, P.E.: Combinatorial group theory. Ergebnisse der Mathematik und ihrer Grenzgebiete, Bd. 89. Berlin, Heidelberg, New York: Springer 1977
Magnus, W.: Diskontinuierliche Gruppen mit einer definierenden Relation. J. Reine Angew. Math.103, 141–165 (1930)
Papakyriakopoulos, Ch.D.: Attaching 2-dimensional cells to a complex. Ann. Math.78, 205–222 (1963)
Ratcliffe, J.G.: Free and projective crossed modules. J. London Math. Soc. (2),22, 66–74 (1980)
Rourke, C.P.: Presentations and the trivial group. In: Topology of low-dimensional manifolds, pp. 134–143. Proceedings Sussex 1977, R. Fenn, ed. Lecture Notes in Mathematics, Vol. 722. Berlin, Heidelberg, New York: Springer 1979
Rourke, C.P., Sanderson, B.J.: Introduction to piecewise linear topology. Ergebnisse der Mathematik und ihrer Grenzgebiete, Bd. 69. Berlin, Heidelberg, New York: Springer 1972
Sieradski, A.J.: Framed links for Pfeiffer identities. Math. Z.175, 125–137 (1980)
Stefan, P.: On Pfeiffer transformations, link diagrams and a question of J.H.C. Whitehead. In: Low-dimensional topology, Proc. Bangor Symp. 1979. R. Brown and T.L. Thickstun, eds. London Math. Soc. Lecture Note Series. Cambridge: Cambridge University Press (1981) (to appear)
Waldhausen, F.: On irreducible 3-manifolds which are sufficiently large. Ann. Math.87, 56–88 (1968)
Whitehead, J.H.C.: On adding relations to homotopy groups. Ann. Math.42, 409–428 (1941)
Whitehead, J.H.C.: Note on the previous paper. Ann. Math.47, 806–810 (1946)
Whitehead, J.H.C.: Combinatorial homotopy. II. Bull. Am. Math. Soc.55, 453–496 (1949)
Whitehead, J.H.C.: Simple homotopy types. Am. J. Math.72, 1–57 (1950)
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Dedicated to the memory of my good friend and colleague Peter Stefan
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Huebschmann, J. Aspherical 2-complexes and an unsettled problem of J. H. C. Whitehead. Math. Ann. 258, 17–37 (1981). https://doi.org/10.1007/BF01450344
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DOI: https://doi.org/10.1007/BF01450344