Groups of polynomial growth and expanding maps (with an appendix by Jacques Tits)

Michael Gromov

Publications Mathématiques de l'IHÉS (1981)

  • Volume: 53, page 53-78
  • ISSN: 0073-8301

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Gromov, Michael. "Groups of polynomial growth and expanding maps (with an appendix by Jacques Tits)." Publications Mathématiques de l'IHÉS 53 (1981): 53-78. <http://eudml.org/doc/103974>.

@article{Gromov1981,
author = {Gromov, Michael},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {finitely generated group of polynomial growth; nilpotent subgroup of finite index; expanding homeomorphism; compact Riemannian manifold},
language = {eng},
pages = {53-78},
publisher = {Institut des Hautes Études Scientifiques},
title = {Groups of polynomial growth and expanding maps (with an appendix by Jacques Tits)},
url = {http://eudml.org/doc/103974},
volume = {53},
year = {1981},
}

TY - JOUR
AU - Gromov, Michael
TI - Groups of polynomial growth and expanding maps (with an appendix by Jacques Tits)
JO - Publications Mathématiques de l'IHÉS
PY - 1981
PB - Institut des Hautes Études Scientifiques
VL - 53
SP - 53
EP - 78
LA - eng
KW - finitely generated group of polynomial growth; nilpotent subgroup of finite index; expanding homeomorphism; compact Riemannian manifold
UR - http://eudml.org/doc/103974
ER -

References

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  1. [1] L. AUSLANDER, E. SCHENKMAN, Free groups and Hirsch-Plotkin radicals, Proc. A.M.S., 16 (1965), 784-788. Zbl0132.01205MR31 #4830
  2. [2] J. CHEEGER, D. EBIN, Comparison theorems in Riemannian geometry, North-Holland, 1975. Zbl0309.53035MR56 #16538
  3. [3] V. EFREMOVIČ, The proximity geometry of Riemannian manifolds, Uspehi Mat. Nauk, 8 (1953), 189 (Russian). Zbl0152.39201
  4. [4] D. EPSTEIN, M. SHUB, Expanding endomorphisms of flat manifolds, Topology, 7 (1968), 13-141. Zbl0157.30403MR37 #3580
  5. [5] M. GROMOV, Synthetic geometry of Riemannian manifolds, Proc. I.C.M. Helsinki, 1978, vol. I, 415-419 (1979). Zbl0427.53018MR81g:53029
  6. [6] M. HIRSCH, Expanding maps and transformation groups, Proc. Symp. Pure Math., XIV (1970), 125-133. Zbl0223.58009MR45 #7750
  7. [7] W. HUREWICZ, H. WALLMAN, Dimension Theory, Princeton U. Press, 1948. Zbl0036.12501
  8. [8] J. MILNOR, A note on curvature and fundamental group, J. Diff. Geom., 2 (1968), 1-7. Zbl0162.25401MR38 #636
  9. [9] D. MONTGOMERY, L. ZIPPIN, Topological transformation groups, Interscience, N. Y., 1955. Zbl0068.01904MR17,383b
  10. [10] M. RAGHUNATHAN, Discrete subgroups of Lie groups, Springer, Berlin, 1972. Zbl0254.22005MR58 #22394a
  11. [11] M. SHUB, Expanding maps, Proc. Symp. Pure Math. XIV (1970), 273-277. Zbl0213.50302MR42 #1158
  12. [12] A. ŠVARC, A volume invariant of coverings, Dokl. Akad. Nauk SSSR, 105 (1955), 32-34. MR17,781d
  13. [13] J. TITS, Free subgroups in linear groups, J. Algebra, 20 (1972), 250-270. Zbl0236.20032MR44 #4105
  14. [14] J. WOLF, Growth of finitely generated solvable groups and curvature of Riemannian manifolds, J. Diff. Geom., 2 (1968), 421-446. Zbl0207.51803MR40 #1939

Citations in EuDML Documents

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  1. Pierre Pansu, Effondrement des variétés riemanniennes
  2. V.I. Trofimov, Undirected and directed graphs with near polynomial growth
  3. Nicolas Th. Varopoulos, Brownian motion and transient groups
  4. Conrad Plaut, A metric characterization of manifolds with boundary
  5. Thierry Coulhon, Laurent Saloff-Coste, Puissances d'un opérateur régularisant
  6. Y. Derriennic, Entropie, théorèmes limite et marches aléatoires
  7. Jean-Pierre Demailly, Thomas Peternell, Michael Schneider, Kähler manifolds with numerically effective Ricci class
  8. P. Pansu, Effondrement des variétés riemanniennes
  9. Michael Gromov, Volume and bounded cohomology
  10. Alexander Fel'shtyn, Richard Hill, Dynamical zeta functions, congruences in Nielsen theory and Reidemeister torsion

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