Isometries, rigidity and universal covers

Annals of Mathematics

Volumn 168, Issue 3, 2008, Pages 915-940

  Farb, Benson ^a   Weinberger, Shmuel ^a  

^a UNIVERSITY OF CHICAGO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 71249099021     PISSN: 0003486X     EISSN: None     Source Type: Journal    
DOI: 10.4007/annals.2008.168.915     Document Type: Article

References (36)

1. A. Assadi, Finite Group Actions on Simply-Connected Manifolds and CW Com-plexes, Mem. Amer. Math. Soc. 35, A.M.S., Providence, RI (1982).
2. P. Baum, A. Connes, and N. Higson, Classifying space for proper actions and K-theory of group C*-algebras, in C*-algebras: 1943-1993, Contemp. Math. 167 (1993), 240-291, A.M.S., Providence, RI, 1994.
3. N. Brady and B. Farb, Filling-invariants at in nity for manifolds of nonpositive curvature, Trans. Amer. Math. Soc. 350 (1998), 3393-3405.
4. R. Bieri, Homological dimension of discrete groups, Queen Mary College Mathematics Notes, London, 1976.
5. A. Borel, Compact Cli ord-Klein forms of symmetric spaces, Topology 2 (1963), 111-122.
6. G. Bredon, Introduction to Compact Transformation Groups, Pure and Applied Math. 46, Academic Press, New York, 1972.
7. M. Bridson, Controlled embeddings into groups that have no non-trivial nite quotients, in The Epstein Birthday Schrift, Geom. Topol. Monogr. 1 (1998), 99-116.
8. K. Brown, Cohomology of groups, Grad. Texts Math. 87, Springer-Verlag, New York, 1982.
9. J. Block and S. Weinberger, Large scale homology theories and geometry, AMS/IP Stud. in Adv. Math. 2 (1997), 522-569.
10. C. Connell and B. Farb, The degree theorem in higher rank, J. Differential Geom. 65 (2003), 19-59.
11. 2 cohomology and group cohomology, Topology 25 (1986), 189-215.
12. P. E. Conner and F. Raymond, Manifolds with few periodic homeomorphisms, in Proc. of the Second Conference on Compact Transformation Groups, Part II, 1-75, Lecture Notes in Math. 299, Springer-Verlag, New York, 1972.
13. M. Davis, Groups generated by reflections and aspherical manifolds not covered by Euclidean space, Ann. of Math. 117 (1983), 293-324.
14. P. Eberlein, Lattices in spaces of nonpositive curvature, Ann. of Math. 111 (1980), 435-476.
15. P. Eberlein, Isometry groups of simply connected manifolds of nonpositive curvature. II, Acta Math. 149 (1982), 41-69.
16. W. Fulton and J. Harris, Representation theory: A first course, Grad. Texts Math. 129, Springer-Verlag, New York, 1991.
17. S. Frankel, Complex geometry of convex domains that cover varieties, Acta Math. 163 (1989), 109-149.
18. S. Frankel, Locally symmetric and rigid factors for complex manifolds via harmonic maps, Ann. of Math. 141 (1995), 285-300.
19. B. Farb and S. Weinberger, Hidden symmetries and arithmetic manifolds, in Geometry, Spectral Theory, Groups, and Dynamics, 111-119, Contemp. Math. 387, A. M. S., Providence, RI, 2005.
20. M. Gromov, Filling Riemannian manifolds, J. Differential Geom. 18 (1983), 1-147.
21. P. de la Harpe, Topics in Geometric Group Theory, Chicago Lectures in Math. Univ. of Chicago Press, Chicago, IL, 2000.
22. S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces, Grad. Studies in Math. 34, A.M.S., Providence, RI, 2001.
23. B. Iversen, Cohomology of Sheaves, Universitext, Springer-Verlag, New York, 1986.
24. K. Iwasawa, On some types of topological groups, Ann. of Math. 50 (1949), 507-558.
25. 2-Invariants: Theory and Applications to Geometry and K-Theory, Ergebnisse der Mathematik, Springer-Verlag, New York, 2002.
26. G. Margulis, Discrete Subgroups of Semisimple Lie Groups, Springer-Verlag, New York, 1991.
27. K. Melnick, Compact Lorentz manifolds with symmetry, Ph.D. thesis, University of Chicago, May 2006.
28. S. B. Myers and N. Steenrod, The group of isometries of a Riemannian manifold, Ann. of Math. 40 (1939), 400-416.
29. A. Nadel, Semisimplicity of the group of biholomorphisms of the universal covering of a compact complex manifold with ample canonical bundle, Ann. of Math. 132 (1990), 193-211.
30. R. Oliver, A proof of the Conner conjecture, Ann. of Math. 103 (1976), 637-644.
31. A.Y. Olshanskii, On residualing homomorphisms and G-subgroups of hyperbolic groups, Internat. J. Algebra Comput. 3 (1993), 365-409.
32. G. Prasad, Discrete subgroups isomorphic to lattices in Lie groups, Amer. J. Math. 98 (1976), 853-863.
33. M. S. Raghunathan, Discrete Subgroups of Lie Groups, Ergebnisse der Mathematik, Springer-Verlag, New York, 1972.
34. J. Stallings, The piecewise-linear structure of Euclidean space, Proc. Cambridge Philos. Soc. 58 (1962), 481-488.
35. R. Schoen and S. T. Yau, Compact group actions and the topology of manifolds with nonpositive curvature, Topology 18 (1979), 361-380.
36. R. Zimmer, Ergodic Theory and Semisimple Groups, Monographs in Math. 81, Birkhäuser, Basel, 1984.