Gromov, Mikhael [Tits, Jacques] Groups of polynomial growth and expanding maps. Appendix by Jacques Tits. (English) Zbl 0474.20018 Publ. Math., Inst. Hautes Étud. Sci. 53, 53-78 (1981). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 31 ReviewsCited in 718 Documents MSC: 20F05 Generators, relations, and presentations of groups 20F34 Fundamental groups and their automorphisms (group-theoretic aspects) 20E07 Subgroup theorems; subgroup growth 20E25 Local properties of groups 20F18 Nilpotent groups Keywords:finitely generated group of polynomial growth; nilpotent subgroup of finite index; expanding homeomorphism; compact Riemannian manifold × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML References: [1] L. Auslander, E. Schenkman, Free groups and Hirsch-Plotkin radicals,Proc. A.M.S.,16 (1965), 784–788. · Zbl 0132.01205 · doi:10.1090/S0002-9939-1965-0180596-7 [2] J. Cheeger, D. Ebin,Comparison theorems in Riemannian geometry, North-Holland, 1975. · Zbl 0309.53035 [3] V. Efremovič, The proximity geometry of Riemannian manifolds,Uspehi Mat. Nauk,8 (1953), 189 (Russian). [4] D. Epstein, M. Shub, Expanding endomorphisms of flat manifolds,Topology,7 (1968), 13–141. · Zbl 0157.30403 · doi:10.1016/0040-9383(68)90022-0 [5] M. Gromov, Synthetic geometry of Riemannian manifolds,Proc. I.C.M. Helsinki, 1978, vol. I, 415–419 (1979). [6] M. Hirsch, Expanding maps and transformation groups,Proc. Symp. Pure Math., XIV (1970), 125–133. · Zbl 0223.58009 [7] W. Hurewicz, H. Wallman,Dimension Theory, Princeton U. Press, 1948. · Zbl 0036.12501 [8] J. Milnor, A note on curvature and fundamental group,J. Diff. Geom.,2 (1968), 1–7. · Zbl 0162.25401 [9] D. Montgomery, L. Zippin,Topological transformation groups, Interscience, N. Y., 1955. · Zbl 0068.01904 [10] M. Raghunathan,Discrete subgroups of Lie groups, Springer, Berlin, 1972. · Zbl 0254.22005 [11] M. Shub, Expanding maps,Proc. Symp. Pure Math. XIV (1970), 273–277. · Zbl 0213.50302 [12] A. Švarc, A volume invariant of coverings,Dokl. Akad. Nauk SSSR,105 (1955), 32–34. · Zbl 0066.15903 [13] J. Tits, Free subgroups in linear groups,J. Algebra,20 (1972), 250–270. · Zbl 0236.20032 · doi:10.1016/0021-8693(72)90058-0 [14] J. Wolf, Growth of finitely generated solvable groups and curvature of Riemannian manifolds,J. Diff. Geom.,2 (1968), 421–446. · Zbl 0207.51803 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.