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On uniform exponential growth for linear groups

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References

  1. Alperin, R., Noskov, G.A.: Uniform growth, actions on trees and GL2. Computational and statistical group theory (Las Vegas, NV, Hoboken, NJ, 2001), pp. 1–5. Contemp. Math., vol. 298. Am. Math. Soc.

  2. Borel, A.: Linear algebraic groups, 2nd ed. math. New York: Springer 1991

  3. Danilov, V.I.: Algebraic varieties and schemes, pp. 167–297. In: Algebraic geometry, I. Berlin: Springer 1994

  4. Delzant, T.: Sous-groupes distingués et quotients des groupes hyperboliques. Duke Math. J. 83, 661–682 (1996)

    Article  MathSciNet  Google Scholar 

  5. de la Harpe, P.: Topics in Geometric Group Theory. Chicago Lec. Math. 2000

  6. Eskin, A., Mozes, S., Oh, H.: Uniform exponential growth of linear groups. Int. Math. Res. Not. 31, 1675–1683 (2002)

    Article  MathSciNet  Google Scholar 

  7. Fulton, W.: Intersection theory, second ed. Berlin: Springer 1998

  8. Grigorchuk, R.I., de la Harpe, P.: On problems related to growth, entropy, and spectrum in group theory. J. Dynam. Control Systems 3, 51–89 (1997)

    Article  MathSciNet  Google Scholar 

  9. Gromov, M.: Structures métriques pour les variétés riemanniennes, ed. by J. Lafontaine, P. Pansu. Paris: CEDIC 1981

  10. Grunewald, F., Segal, D.: Remarks on injective specializations. J. Algebra 61, 538–547 (1979)

    Article  MathSciNet  Google Scholar 

  11. Koblitz, N.: p-adic Numbers, p-adic Analysis and Zeta Functions. Grad. Texts Math. 58. New York: Springer 1984

  12. Koubi, M.: Croissance uniforme dans les groupes hyperboliques. Ann. Inst. Fourier (Grenoble) 48, 1441–1453 (1998)

    Article  MathSciNet  Google Scholar 

  13. Lubotzky, A., Mann, A.: On groups of polynomial subgroup growth. Invent. Math. 104, 521–533 (1991)

    Article  MathSciNet  Google Scholar 

  14. Manning, A.: Topological entropy for geodesic flows. Ann. Math. 110, 567–573 (1979)

    Article  MathSciNet  Google Scholar 

  15. Milnor, J.: Growth of finitely generated solvable groups. J. Differ. Geom. 2, 447–449 (1968)

    MathSciNet  Google Scholar 

  16. Osin, D.: The entropy of solvable groups. Ergodic Theory Dyn. Syst. 23, 907–918 (2003)

    Article  MathSciNet  Google Scholar 

  17. Raghunathan, M.S.: Discrete subgroups of Lie groups. New York: Springer 1972

  18. Shalen, P., Wagreich, P.: Growth rates, ℤ p -homology, and volumes of hyperbolic 3-manifolds. Trans. Am. Math. Soc. 331, 895–917 (1992)

    MathSciNet  Google Scholar 

  19. Schinzel, A.: Polynomials with special regard to reducibility. With an appendix by Umberto Zannier. Cambridge: Cambridge University Press 2000

  20. Selberg, A.: On discontinuous groups in higher-dimensional symmetric spaces. Contributions to function theory (Internat. Colloq. Function Theory, Bombay, 1960), pp. 147–164. Bombay: Tata Institute of Fundamental Research 1960

  21. Tits, J.: Free subgroups in linear groups. J. Algebra 20, 250–270 (1972)

    Article  MathSciNet  Google Scholar 

  22. Wilson, J.: Preprint 2000

  23. Wilson, J.: On exponential growth and uniformly exponential growth for groups. Invent. Math. 155, 287–303 (2004)

    Article  MathSciNet  Google Scholar 

  24. Wolf, J.A.: Growth of finitely generated solvable groups and curvature of Riemanniann manifolds. J. Differ. Geom. 2, 421–446 (1968)

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Chicago, Chicago, IL, 60637, USA

    Alex Eskin

  2. Institute of Mathematics, Hebrew University, Jerusalem, 91904, Israel

    Shahar Mozes

  3. Department of Mathematics, Princeton University, Princeton, NJ, USA

    Hee Oh

  4. Institute for Advanced Study, Einstein Drive, Princeton, NJ, USA

    Hee Oh

Authors
  1. Alex Eskin
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  2. Shahar Mozes
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  3. Hee Oh
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Correspondence to Alex Eskin or Shahar Mozes.

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Eskin, A., Mozes, S. & Oh, H. On uniform exponential growth for linear groups. Invent. math. 160, 1–30 (2005). https://doi.org/10.1007/s00222-004-0378-z

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