A Fixed point theorem for periodic maps on locally symmetric manifolds

Weinberger, S.

doi:10.1090/spmj/1481

A Fixed point theorem for periodic maps on locally symmetric manifolds
HTML articles powered by AMS MathViewer

by S. Weinberger

St. Petersburg Math. J. 29 (2018), 43-50

DOI: https://doi.org/10.1090/spmj/1481

Published electronically: December 27, 2017

PDF | Request permission

Abstract:

Some fixed point results indicated in the title are established.

References

M. F. Atiyah and G. B. Segal, The index of elliptic operators. II, Ann. of Math. (2) 87 (1968), 531–545. MR 236951, DOI 10.2307/1970716
Paul Baum, Alain Connes, and Nigel Higson, Classifying space for proper actions and $K$-theory of group $C^\ast$-algebras, $C^\ast$-algebras: 1943–1993 (San Antonio, TX, 1993) Contemp. Math., vol. 167, Amer. Math. Soc., Providence, RI, 1994, pp. 240–291. MR 1292018, DOI 10.1090/conm/167/1292018
Jonathan Block and Shmuel Weinberger, Arithmetic manifolds of positive scalar curvature, J. Differential Geom. 52 (1999), no. 2, 375–406. MR 1758300
Armand Borel, Œuvres: collected papers. Vol. II, Springer-Verlag, Berlin, 1983 (French). 1959–1968. MR 725853
Armand Borel, Seminar on transformation groups, Annals of Mathematics Studies, No. 46, Princeton University Press, Princeton, N.J., 1960. With contributions by G. Bredon, E. E. Floyd, D. Montgomery, R. Palais. MR 0116341
J. Bryant, S. Ferry, W. Mio, and S. Weinberger, Topology of homology manifolds, Ann. of Math. (2) 143 (1996), no. 3, 435–467. MR 1394965, DOI 10.2307/2118532
Sylvain E. Cappell and Julius L. Shaneson, Nonlinear similarity, Ann. of Math. (2) 113 (1981), no. 2, 315–355. MR 607895, DOI 10.2307/2006986
Stanley S. Chang and Shmuel Weinberger, Topological nonrigidity of nonuniform lattices, Comm. Pure Appl. Math. 60 (2007), no. 2, 282–290. MR 2275330, DOI 10.1002/cpa.20151
Michael W. Davis, Groups generated by reflections and aspherical manifolds not covered by Euclidean space, Ann. of Math. (2) 117 (1983), no. 2, 293–324. MR 690848, DOI 10.2307/2007079
Allan L. Edmonds and Ronnie Lee, Compact Lie groups which act on Euclidean space without fixed points, Proc. Amer. Math. Soc. 55 (1976), no. 2, 416–418. MR 420672, DOI 10.1090/S0002-9939-1976-0420672-1
E. E. Floyd and R. W. Richardson, An action of a finite group on an $n$-cell without stationary points, Bull. Amer. Math. Soc. 65 (1959), 73–76. MR 100848, DOI 10.1090/S0002-9904-1959-10282-2
J. Fowler, Thesis, Univ. Chicago, 2011.
W. C. Hsiang and William Pardon, When are topologically equivalent orthogonal transformations linearly equivalent?, Invent. Math. 68 (1982), no. 2, 275–316. MR 666164, DOI 10.1007/BF01394060
G. G. Kasparov, Equivariant $KK$-theory and the Novikov conjecture, Invent. Math. 91 (1988), no. 1, 147–201. MR 918241, DOI 10.1007/BF01404917
Steven P. Kerckhoff, The Nielsen realization problem, Ann. of Math. (2) 117 (1983), no. 2, 235–265. MR 690845, DOI 10.2307/2007076
I. Madsen and M. Rothenberg, On the classification of $G$-spheres. I. Equivariant transversality, Acta Math. 160 (1988), no. 1-2, 65–104. MR 926525, DOI 10.1007/BF02392273
Robert Oliver, Fixed-point sets of group actions on finite acyclic complexes, Comment. Math. Helv. 50 (1975), 155–177. MR 375361, DOI 10.1007/BF02565743
Jonathan Rosenberg and Shmuel Weinberger, An equivariant Novikov conjecture, $K$-Theory 4 (1990), no. 1, 29–53. With an appendix by J. P. May. MR 1076524, DOI 10.1007/BF00534192
Jonathan Rosenberg and Shmuel Weinberger, Higher $G$-signatures for Lipschitz manifolds, $K$-Theory 7 (1993), no. 2, 101–132. MR 1235284, DOI 10.1007/BF00962083
Richard Schoen and Shing Tung Yau, Compact group actions and the topology of manifolds with nonpositive curvature, Topology 18 (1979), no. 4, 361–380. MR 551017, DOI 10.1016/0040-9383(79)90026-0
Graeme Segal, Equivariant $K$-theory, Inst. Hautes Études Sci. Publ. Math. 34 (1968), 129–151. MR 234452
Nicolae Teleman, The index of signature operators on Lipschitz manifolds, Inst. Hautes Études Sci. Publ. Math. 58 (1983), 39–78 (1984). MR 720931
S. Weinberger, Variations on a theme of Borel, 2016, Preprint; Cambridge Univ. Press (to appear).
Shmuel Weinberger, Group actions and higher signatures, Proc. Nat. Acad. Sci. U.S.A. 82 (1985), no. 5, 1297–1298. MR 873231, DOI 10.1073/pnas.82.5.1297