A fixed point theorem for simplicial complexes whose fundamental groups are free products

Raymond, Frank

doi:10.1090/S0002-9939-1984-0722427-1

A fixed point theorem for simplicial complexes whose fundamental groups are free products
HTML articles powered by AMS MathViewer

by Frank Raymond PDF

Proc. Amer. Math. Soc. 90 (1984), 111-117 Request permission

Abstract:

A fixed point theorem for actions of toral and finite $p$-groups is obtained for finite simplicial complexes satisfying certain conditions on their fundamental groups and their universal covering spaces. Examples are constructed relating this result to other well-known results.

References

Edward M. Bloomberg, Manifolds with no periodic homeomorphisms, Trans. Amer. Math. Soc. 202 (1975), 67–78. MR 358842, DOI 10.1090/S0002-9947-1975-0358842-7
Daniel E. Cohen, Groups of cohomological dimension one, Lecture Notes in Mathematics, Vol. 245, Springer-Verlag, Berlin-New York, 1972. MR 0344359
P. E. Conner, On the action of the circle group, Michigan Math. J. 4 (1957), 241–247. MR 96747
P. E. Conner and Frank Raymond, Manifolds with few periodic homeomorphisms, Proceedings of the Second Conference on Compact Transformation Groups (Univ. Massachusetts, Amherst, Mass., 1971) Lecture Notes in Math., Vol. 299, Springer, Berlin, 1972, pp. 1–75. MR 0358835
P. E. Conner and Frank Raymond, Actions of compact Lie groups on aspherical manifolds, Topology of Manifolds (Proc. Inst., Univ. of Georgia, Athens, Ga., 1969) Markham, Chicago, Ill., 1970, pp. 227–264. MR 0271958
P. E. Conner and Frank Raymond, Deforming homotopy equivalences to homeomorphisms in aspherical manifolds, Bull. Amer. Math. Soc. 83 (1977), no. 1, 36–85. MR 467777, DOI 10.1090/S0002-9904-1977-14179-7
D. B. A. Epstein, Ends, Topology of 3-manifolds and related topics (Proc. The Univ. of Georgia Institute, 1961) Prentice-Hall, Englewood Cliffs, N.J., 1962, pp. 110–117. MR 0158380
E. E. Floyd, Fixed point sets of compact abelian Lie groups of transformations, Ann. of Math. (2) 66 (1957), 30–35. MR 88733, DOI 10.2307/1970115
Ronnie Lee and Frank Raymond, Manifolds covered by Euclidean space, Topology 14 (1975), 49–57. MR 365581, DOI 10.1016/0040-9383(75)90034-8
Frank Raymond, The end point compactification of manifolds, Pacific J. Math. 10 (1960), 947–963. MR 120637
Frank Raymond, Classification of the actions of the circle on $3$-manifolds, Trans. Amer. Math. Soc. 131 (1968), 51–78. MR 219086, DOI 10.1090/S0002-9947-1968-0219086-9
Reinhard Schultz, Group actions on hypertoral manifolds. II, J. Reine Angew. Math. 325 (1981), 75–86. MR 618547, DOI 10.1515/crll.1981.325.75
John R. Stallings, On torsion-free groups with infinitely many ends, Ann. of Math. (2) 88 (1968), 312–334. MR 228573, DOI 10.2307/1970577