A fixed point theorem for periodic maps on locally symmetric manifolds
Algebra i analiz, Tome 29 (2017) no. 1, pp. 60-69.

Voir la notice de l'article provenant de la source Math-Net.Ru

Some fixed point results indicated in the title are established.
Keywords: aspherical manifolds, rigidity theorems, Borel conjecture, Smith theory.
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S. Weinberger. A fixed point theorem for periodic maps on locally symmetric manifolds. Algebra i analiz, Tome 29 (2017) no. 1, pp. 60-69. http://geodesic.mathdoc.fr/item/AA_2017_29_1_a3/

[1] Atiyah M., Segal G., “The index of elliptic operators. II”, Ann. of Math. (2), 87 (1968), 531–545 | DOI | MR | Zbl

[2] Baum P., Connes A., Higson N., “Classifying space for proper actions and $K$-theory of group $C*$-algebras”, Contemp. Maths., 167, Amer. Math. Soc., Providence, RI, 1994, 240–291 | DOI | MR

[3] Block J., Weinberger S., “Arithmetic manifolds of positive scalar curvature”, J. Differential Geom., 52:2 (1999), 375–406 | DOI | MR | Zbl

[4] Borel A., Oeuvres: collected papers, v. II, 1959–1968, Springer, Heidelberg, 1983 | MR | Zbl

[5] Borel A., Seminar on transformation groups, Ann. of Math. Stud., 46, Princeton Univ. Press, Princeton, NJ, 1960 | MR | Zbl

[6] Bryant J., Ferry S., Mio W., Weinberger S., “The topology of homology manifolds”, Ann. of Math. (2), 143:3 (1996), 435–467 | DOI | MR | Zbl

[7] Cappell S., Shaneson J., “Nonlinear similiarity”, Ann. of Math. (2), 113:2 (1981), 315–355 | DOI | MR | Zbl

[8] Chang S., Weinberger S., “Topological nonrigidity of nonuniform lattices”, Comm. Pure Appl. Math., 60:2 (2007), 282–290 | DOI | MR | Zbl

[9] Davis M., “Groups generated by reflections and aspherical manifolds not covered by Euclidean space”, Ann. of Math. (2), 117:2 (1983), 293–324 | DOI | MR | Zbl

[10] Edmonds A., Lee R., “Compact Lie groups which act on Euclidean space without fixed points”, Proc. Amer. Math. Soc., 55:2 (1976), 416–418 | DOI | MR | Zbl

[11] Floyd E., Richardson R., “An action of a finite group on an $n$-cell without stationary points”, Bull. Amer. Math. Soc., 65 (1959), 73–76 | DOI | MR | Zbl

[12] Fowler J., Thesis, Univ. Chicago, 2011

[13] Hsiang W. C., Pardon W., “When are topologically equivalent orthogonal transformations linearly equivalent?”, Invent. Math., 68:2 (1982), 275–316 | DOI | MR | Zbl

[14] Kasparov G., “Equivariant $KK$-theory and the Novikov conjecture”, Invent. Math., 91:1 (1988), 147–201 | DOI | MR | Zbl

[15] Kerckhoff S., “Nielsen realization problem”, Ann. of Math. (2), 117:2 (1983), 235–265 | DOI | MR | Zbl

[16] Madsen I., Rothenberg M., “On the classification of $G$-spheres. I. Equivariant transversality”, Acta Math., 160:1–2 (1988), 65–104 | DOI | MR | Zbl

[17] Oliver R., “Fixed-point sets of group actions on finite acyclic complexes”, Comment. Math. Helv., 50 (1975), 155–177 | DOI | MR | Zbl

[18] Rosenberg J., Weinberger S., “An equivariant Novikov conjecture”, $K$-Theory, 4:1 (1990), 29–53 | DOI | MR | Zbl

[19] Rosenberg J., Weinberger S., “Higher $G$-signatures for Lipschitz manifolds”, $K$-Theory, 7:2 (1993), 101–132 | DOI | MR | Zbl

[20] Schoen R., Yau S. T., “Compact group actions and the topology of manifolds with nonpositive curvature”, Topology, 18:4 (1979), 361–80 | DOI | MR

[21] Segal G., “Equivariant $K$-theory”, Inst. Hautes Études Sci. Publ. Math., 34 (1968), 129–151 | DOI | MR | Zbl

[22] Teleman N., “The index of signature operators on Lipschitz manifolds”, Inst. Hautes Études Sci. Publ. Math., 58 (1983), 39–78 | DOI | MR

[23] Weinberger S., Variations on a theme of Borel, Preprint, Cambridge Univ. Press, 2016 (to appear)

[24] Weinberger S., “Group actions and higher signatures”, Proc. Nat. Acad. Sci. USA, 82:5 (1985), 1297–1298 | DOI | MR | Zbl