A fixed point theorem for simplicial complexes whose fundamental groups are free products
Author:
Frank Raymond
Journal:
Proc. Amer. Math. Soc. 90 (1984), 111117
MSC:
Primary 57S10; Secondary 57S17
MathSciNet review:
722427
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Abstract 
References 
Similar Articles 
Additional Information
Abstract: A fixed point theorem for actions of toral and finite 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 wellknown results.
 [B]
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Amer. Math. Soc. 83 (1977), no. 1, 36–85. MR 0467777
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Lee and Frank
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(51 #1833)
 [R1]
Frank
Raymond, The end point compactification of manifolds, Pacific
J. Math. 10 (1960), 947–963. MR 0120637
(22 #11387)
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circle on 3manifolds, Trans. Amer. Math.
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0219086 (36 #2169), http://dx.doi.org/10.1090/S00029947196802190869
 [S]
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Angew. Math. 325 (1981), 75–86. MR 618547
(82m:57022), http://dx.doi.org/10.1515/crll.1981.325.75
 [St]
John
R. Stallings, On torsionfree groups with infinitely many
ends, Ann. of Math. (2) 88 (1968), 312–334. MR 0228573
(37 #4153)
 [B]
 Edward M. Bloomberg, Manifolds with no periodic homeomorphisms, Trans. Amer. Math. Soc. 202 (1975), 6778. MR 0358842 (50:11301)
 [Cohen]
 Daniel E. Cohen, Groups of cohomological dimension one, Lecture Notes in Math., vol. 245, SpringerVerlag, Berlin and New York, 1972. MR 0344359 (49:9098)
 [C]
 P. E. Conner, On the action of the circle group, Michigan Math. J. 4 (1957), 241248. MR 0096747 (20:3230)
 [CR1]
 P. E. Conner and Frank Raymond, Manifolds with few periodic homeomorphisms, Proc. Second Conf. Compact Transformation Groups, Lecture Notes in Math., vol. 299, SpringerVerlag, Berlin and New York, 1972, pp. 175. MR 0358835 (50:11294)
 [CR2]
 , Actions of compact Lie groups on aspherical manifolds, Topology of Manifolds (Cantrell and Edwards, eds.), Markham, Chicago, Ill., 1970, pp. 227264. MR 0271958 (42:6839)
 [CR3]
 , Deforming homotopy equivalences to homeomorphisms in aspherical manifolds, Bull. Amer. Math. Soc. 83 (1977), 3685. MR 0467777 (57:7629)
 [E]
 D. B. A. Epstein, Ends, topology of manifolds (M. K. Fort, Jr., ed.), PrenticeHall, Englewood Cliffs, N.J., 1962, pp. 110117. MR 0158380 (28:1605)
 [F]
 E. E. Floyd, Fixed point sets of compact abelian Lie groups, Ann. of Math. (2) 66 (1957), 3035. MR 0088733 (19:571e)
 [LR]
 Ronnie Lee and Frank Raymond, Manifolds covered by Euclidean space, Topology 14 (1975), 4957. MR 0365581 (51:1833)
 [R1]
 Frank Raymond, The end point compactification of manifolds, Pacific J. Math. 10 (1960), 947963. MR 0120637 (22:11387)
 [R2]
 , Classification of the actions of the circle on manifolds, Trans. Amer. Math. Soc. 131 (1968), 5178. MR 0219086 (36:2169)
 [S]
 Reinhard Schultz, Group actions on hypertoral manifolds. II, J. Reine Angew Math. 325 (1981), 7586. MR 618547 (82m:57022)
 [St]
 J. R. Stallings, On torsionfree groups with infinitely many ends, Ann. of Math. (2) 88 (1968), 312334. MR 0228573 (37:4153)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939198407224271
PII:
S 00029939(1984)07224271
Keywords:
Transformation groups,
covering spaces,
ends,
Freudenthal compactification,
clc,
cohomology groups,
simplicial complex,
fundamental group,
free products,
fixed points
Article copyright:
© Copyright 1984
American Mathematical Society
