Groups of polynomial growth and expanding maps

  • Mikhael Gromov
Article

Keywords

Riemannian Manifold Nilpotent Group Hausdorff Distance Solvable Group Finite Index 
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References

  1. [1]
    L. Auslander, E. Schenkman, Free groups and Hirsch-Plotkin radicals,Proc. A.M.S.,16 (1965), 784–788.MATHCrossRefGoogle Scholar
  2. [2]
    J. Cheeger, D. Ebin,Comparison theorems in Riemannian geometry, North-Holland, 1975.Google Scholar
  3. [3]
    V. Efremovič, The proximity geometry of Riemannian manifolds,Uspehi Mat. Nauk,8 (1953), 189 (Russian).Google Scholar
  4. [4]
    D. Epstein, M. Shub, Expanding endomorphisms of flat manifolds,Topology,7 (1968), 13–141.CrossRefGoogle Scholar
  5. [5]
    M. Gromov, Synthetic geometry of Riemannian manifolds,Proc. I.C.M. Helsinki, 1978, vol. I, 415–419 (1979).Google Scholar
  6. [6]
    M. Hirsch, Expanding maps and transformation groups,Proc. Symp. Pure Math., XIV (1970), 125–133.Google Scholar
  7. [7]
    W. Hurewicz, H. Wallman,Dimension Theory, Princeton U. Press, 1948.Google Scholar
  8. [8]
    J. Milnor, A note on curvature and fundamental group,J. Diff. Geom.,2 (1968), 1–7.MATHGoogle Scholar
  9. [9]
    D. Montgomery, L. Zippin,Topological transformation groups, Interscience, N. Y., 1955.MATHGoogle Scholar
  10. [10]
    M. Raghunathan,Discrete subgroups of Lie groups, Springer, Berlin, 1972.MATHGoogle Scholar
  11. [11]
    M. Shub, Expanding maps,Proc. Symp. Pure Math. XIV (1970), 273–277.Google Scholar
  12. [12]
    A. Švarc, A volume invariant of coverings,Dokl. Akad. Nauk SSSR,105 (1955), 32–34.Google Scholar
  13. [13]
    J. Tits, Free subgroups in linear groups,J. Algebra,20 (1972), 250–270.MATHCrossRefGoogle Scholar
  14. [14]
    J. Wolf, Growth of finitely generated solvable groups and curvature of Riemannian manifolds,J. Diff. Geom.,2 (1968), 421–446.MATHGoogle Scholar

Copyright information

© Publications Mathématiques de L’I.H.É.S. 1981

Authors and Affiliations

  • Mikhael Gromov
    • 1
  1. 1.Institut des Hautes Études scientifiquesBures-sur-Yvette

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