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Actions of discrete groups on nonpositively curved spaces

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References

  • [Ba1] W. Ballmann: Lectures on spaces of nonpositive curvature, DMV-Seminar vol. 25, Birkhäuser 1995.

  • [Ba2] W. Ballmann: Singular spaces of nonpositive curvature, In: E. Ghys and P. de la Harpe, Sur les groupes hyperboliques d'après Mikhael Gromov, Birkhäuser 1990., pp. 189–201.

  • [BGS] W. Ballmann, M. Gromov, V. Schroeder: Manifolds of nonpositive curvature, Birkhäuser 1985.

  • [Bi] J. Birman: Braids, links and mapping class groups, Annals of Math. Stud.82, Princeton University Press, 1974.

  • [BLM] J. Birman, A. Lubotzky, J. McCarthy: Abelian and solvable subgroups of the mapping class groups, Duke Math. Journal50 (1983) 1107–1120.

    Google Scholar 

  • [BH] M. Bridson and A. Haefliger:CAT (0)-spaces, in preparation.

  • [BK1] S. Buyalo, V. Kobelski: Geometrization of graphmanifolds: conformal states, POMI Preprint no. 7, July 1994. To appear in St. Petersburg Math. J.

  • [BK2] S. Buyalo, V. Kobelski: Geometrization of graphmanifolds: isometric states, POMI Preprint no. 8, October 1994. To appear in St. Petersburg Math. J.

  • [EE] J. Earle, J. Eells: The diffeomorphism group of a compact Riemann surface, Bull. of AMS73 (1967) 557–559.

    Google Scholar 

  • [E] P. Eberlein: A canonical form for compact nonpositively curved manifolds whose fundamental groups have nontrivial center, Math. Ann.260, (1982), vol. 1, 23–29.

    Google Scholar 

  • [Ge1] S. Gersten: The automorphism group of free group is not aCAT (0)-group, University of Utah, Preprint.

  • [Ge2] S. Gersten: Bounded cocycles and combings of groups. Int. J. of Algebra and Computation.2, no. 3 (1992), 307–326.

    Google Scholar 

  • [GW] D. Gromoll, J. Wolf: Some relations between the metric structure and the algebraic structure of the fundamental group in manifolds of nonpositive curvature, Bull. Amer. Math. Soc. 77, vol.4 (1971), 545–552.

    Google Scholar 

  • [He] J. Hempel: 3-manifolds, Annals of Math. Studies, Vol.86, Princeton University Press, 1976.

  • [KL1] M. Kapovich, B. Leeb: Asymptotic cones and quasi-isometry classes of fundamental groups of 3-manifolds, Geometric and Functional Analysis5 (3) (1995), 582–603.

    Google Scholar 

  • [KL2] M. Kapovich, B. Leeb: On actions of discrete groups on nonpositively curved spaces, MSRI-preprint 059-94, 1994.

  • [KL3] M. Kapovich, B. Leeb: On quasi-isometries of graph manifold groups, preprint 1994.

  • [KlL] B. Kleiner, B. Leeb: Rigidity of quasi-isometries for symmetric spaces of higher rank, preprint 1995.

  • [Ko] K. Kodaira: A certain type of irregular algebraic surfaces, J. d'Anal. Math.19 (1967) 207–215.

    Google Scholar 

  • [LY] H. B. Lawson, S. T. Yau: On compact manifolds of nonpositive curvature, J. Diff. Geom.7 (1972), 211–238.

    Google Scholar 

  • [L1] B. Leeb: 3-manifolds with(out) metrics of nonpositive curvature, PhD Thesis, University of Maryland, 1992.

  • [L2] B. Leeb: 3-manifolds with(out) metrics of nonpositive curvature, Invent. Math.122(2) (1995), 277–289.

    Google Scholar 

  • [Me] G. Mess: Unit tangent bundle subgroups of the mapping class group, MSRI-preprint 05708-90, 1990.

  • [Sc] P. Scott: The geometries of 3-manifolds. Bull. London Math. Soc.15 (1983), 404–487.

    Google Scholar 

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This research was partially supported by the NSF grant DMS-9022140 at MSRI (Leeb) and the NSF grant DMS-9306140 (Kapovich).

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Kapovich, M., Leeb, B. Actions of discrete groups on nonpositively curved spaces. Math. Ann. 306, 341–352 (1996). https://doi.org/10.1007/BF01445254

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Mathematics Subject Classification (1991)

  • 20F32
  • 51K10
  • 53C15
  • 57M50