Mathematische Annalen

, Volume 258, Issue 1, pp 17–37

Aspherical 2-complexes and an unsettled problem of J. H. C. Whitehead

  • Johannes Huebschmann


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Adams, J.F.: A new proof of a theorem of W.H. Cockcroft. J. London Math. Soc.30, 482–488 (1955)Google Scholar
  2. 2.
    Beckmann, W.H.: Completely aspherical 2-complexes. Ph.d. thesis, Cornell 1980Google Scholar
  3. 3.
    Beckmann, W.H.: A certain class of non-aspherical 2-complexes. J. Pure Appl. Alg.16, 243–244 (1980)Google Scholar
  4. 4.
    Brandenburg, J., Dyer, M.N.: On the aspherical Whitehead conjecture. Preprint 1979Google Scholar
  5. 5.
    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)Google Scholar
  6. 6.
    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)Google Scholar
  7. 7.
    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)Google Scholar
  8. 8.
    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 1976Google Scholar
  9. 9.
    Cockcroft, W.H.: Note on a theorem due to J.H.C. Whitehead. Quart. J. Math.2, 159–160 (1951)Google Scholar
  10. 10.
    Cockcroft, W.H.: On two-dimensional aspherical complexes. Proc. London Math. Soc. (3)4, 375–384 (1954)Google Scholar
  11. 11.
    Chiswell, I.M., Collins, D.J., Huebschmann, J.: Aspherical group presentations. Math. Z.178, 1–36 (1981)Google Scholar
  12. 12.
    Cohen, J.M.: Aspherical 2-complexes. J. Pure Appl. Alg.12, 101–110 (1978)Google Scholar
  13. 13.
    Collins, D.J., Huebschmann, J.: Spherical diagrams and identities among relations. Preprint 1981Google Scholar
  14. 14.
    Dunwoody, M.J.: Answer to a conjecture of J.M. Cohen, J. Pure Appl. Alg.16, 249 (1980)Google Scholar
  15. 15.
    Fenn, R.: Letter to P. Stefan (unpublished)Google Scholar
  16. 16.
    Gutierrez, M.A., Ratcliffe, J.G.: On the second homotopy group. Quart. J. Math. Oxford (2)32, 45–55 (1081)Google Scholar
  17. 17.
    Hempel, J.: 3-manifolds, Annals of Mathematics Studies, Vol. 86. Princeton: Princeton University Press 1976Google Scholar
  18. 18.
    Hilton, P.J.: An Introduction to homotopy theory. Cambridge: Cambridge University Press 1953Google Scholar
  19. 19.
    Howie, J.: Aspherical and acyclic 2-complexes. J. London Math. Soc. (2)20, 549–558 (1979)Google Scholar
  20. 20.
    Igusa, K.: The generalized Grassmann invariantK 3(ℤ[π])→H 0(π,ℤ2[π]) (preprint)Google Scholar
  21. 21.
    Lyndon, R.C.: Cohomology theory of groups with a single defining relation. Ann. Math.52, 650–665 (1950)Google Scholar
  22. 22.
    Lyndon, R.C.: Dependence and independence in free groups. J. Reine Angew. Math.210, 148–174 (1962)Google Scholar
  23. 23.
    Lyndon, R.C.: On the Freiheitssatz. J. London Math. Soc. (2)5, 95–101 (1972)Google Scholar
  24. 24.
    Lyndon, R.C., Schupp, P.E.: Combinatorial group theory. Ergebnisse der Mathematik und ihrer Grenzgebiete, Bd. 89. Berlin, Heidelberg, New York: Springer 1977Google Scholar
  25. 25.
    Magnus, W.: Diskontinuierliche Gruppen mit einer definierenden Relation. J. Reine Angew. Math.103, 141–165 (1930)Google Scholar
  26. 26.
    Papakyriakopoulos, Ch.D.: Attaching 2-dimensional cells to a complex. Ann. Math.78, 205–222 (1963)Google Scholar
  27. 27.
    Ratcliffe, J.G.: Free and projective crossed modules. J. London Math. Soc. (2),22, 66–74 (1980)Google Scholar
  28. 28.
    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 1979Google Scholar
  29. 29.
    Rourke, C.P., Sanderson, B.J.: Introduction to piecewise linear topology. Ergebnisse der Mathematik und ihrer Grenzgebiete, Bd. 69. Berlin, Heidelberg, New York: Springer 1972Google Scholar
  30. 30.
    Sieradski, A.J.: Framed links for Pfeiffer identities. Math. Z.175, 125–137 (1980)Google Scholar
  31. 31.
    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)Google Scholar
  32. 32.
    Waldhausen, F.: On irreducible 3-manifolds which are sufficiently large. Ann. Math.87, 56–88 (1968)Google Scholar
  33. 33.
    Whitehead, J.H.C.: On adding relations to homotopy groups. Ann. Math.42, 409–428 (1941)Google Scholar
  34. 34.
    Whitehead, J.H.C.: Note on the previous paper. Ann. Math.47, 806–810 (1946)Google Scholar
  35. 35.
    Whitehead, J.H.C.: Combinatorial homotopy. II. Bull. Am. Math. Soc.55, 453–496 (1949)Google Scholar
  36. 36.
    Whitehead, J.H.C.: Simple homotopy types. Am. J. Math.72, 1–57 (1950)Google Scholar

Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • Johannes Huebschmann
    • 1
  1. 1.Mathematisches Institut der UniversitätHeidelbergFederal Republic of Germany

Personalised recommendations