A topological proof of the equivariant Dehn lemma
HTML articles powered by AMS MathViewer
- by Allan L. Edmonds
- Trans. Amer. Math. Soc. 297 (1986), 605-615
- DOI: https://doi.org/10.1090/S0002-9947-1986-0854087-X
- PDF | Request permission
Abstract:
An elementary topological proof is given for a completely general version of the Equivariant Dehn Lemma, in the spirit of the original proof of the nonequivariant version due to C. D. Papakyriakopolous in 1957.References
- John W. Morgan and Hyman Bass (eds.), The Smith conjecture, Pure and Applied Mathematics, vol. 112, Academic Press, Inc., Orlando, FL, 1984. Papers presented at the symposium held at Columbia University, New York, 1979. MR 758459
- Glen E. Bredon, Introduction to compact transformation groups, Pure and Applied Mathematics, Vol. 46, Academic Press, New York-London, 1972. MR 0413144
- M. J. Dunwoody, An equivariant sphere theorem, Bull. London Math. Soc. 17 (1985), no. 5, 437–448. MR 806009, DOI 10.1112/blms/17.5.437
- Allan L. Edmonds, On the equivariant Dehn lemma, Combinatorial methods in topology and algebraic geometry (Rochester, N.Y., 1982) Contemp. Math., vol. 44, Amer. Math. Soc., Providence, RI, 1985, pp. 141–147. MR 813109, DOI 10.1090/conm/044/813109
- Michael Freedman and Shing Tung Yau, Homotopically trivial symmetries of Haken manifolds are toral, Topology 22 (1983), no. 2, 179–189. MR 683759, DOI 10.1016/0040-9383(83)90030-7
- John Hempel, $3$-Manifolds, Annals of Mathematics Studies, No. 86, Princeton University Press, Princeton, N. J.; University of Tokyo Press, Tokyo, 1976. MR 0415619 H. Meeks III and G. P. Scott, Finite groups actions on $3$-manifolds, preprint, 1983.
- William H. Meeks III and Shing Tung Yau, The equivariant Dehn’s lemma and loop theorem, Comment. Math. Helv. 56 (1981), no. 2, 225–239. MR 630952, DOI 10.1007/BF02566211
- C. D. Papakyriakopoulos, On Dehn’s lemma and the asphericity of knots, Ann. of Math. (2) 66 (1957), 1–26. MR 90053, DOI 10.2307/1970113
- Peter Scott, There are no fake Seifert fibre spaces with infinite $\pi _{1}$, Ann. of Math. (2) 117 (1983), no. 1, 35–70. MR 683801, DOI 10.2307/2006970
- Arnold Shapiro and J. H. C. Whitehead, A proof and extension of Dehn’s lemma, Bull. Amer. Math. Soc. 64 (1958), 174–178. MR 103474, DOI 10.1090/S0002-9904-1958-10198-6
Bibliographic Information
- © Copyright 1986 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 297 (1986), 605-615
- MSC: Primary 57M35; Secondary 57N10, 57S17
- DOI: https://doi.org/10.1090/S0002-9947-1986-0854087-X
- MathSciNet review: 854087