Israel Journal of Mathematics

, Volume 88, Issue 1–3, pp 73–124 | Cite as

Representation varieties of arithmetic groups and polynomial periodicity of Betti numbers

  • Scot Adams


We give a method of studying character varieties of arithmetic groups with an application to polynomial periodicity of Betti numbers of manifolds in congruence towers.


Normal Subgroup BETTI Number Closed Subgroup Finite Index Open Subgroup 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [BMS1] H. Bass, J. Milnor and J.-P. Serre,Solution of the congruence subgroup problem for SLn and Sp2n, Publications de l'IHES33 (1967), 59–137.MATHMathSciNetGoogle Scholar
  2. [BoSe1] A. Borel and J.-P. Serre,Théorèmes de finitude en cohomologie galoisienne, Commentarii Mathematici Helvetici39 (1964), 111–164.MATHCrossRefMathSciNetGoogle Scholar
  3. [Bor1] A. Borel,Density and maximality of arithmetic subgroups, Journal für die Reine und Angewandte Mathematik224 (1966), 78–89.MATHMathSciNetCrossRefGoogle Scholar
  4. [Bor2] A. Borel,Introduction aux Groupes Arithmétiques, Hermann, Paris, 1969.MATHGoogle Scholar
  5. [Cor1] K, Corlette,Archimedean superrigidity and hyperbolic geometry, Annals of Mathematics135 (1992), 165–182.CrossRefMathSciNetGoogle Scholar
  6. [CR1] C. Curtis and I. Reiner,Representation Theory of Finite Groups and Associative Algebras, Wiley-Interscience, New York, 1962 (second printing, 1966).MATHGoogle Scholar
  7. [GrSc1] M. Gromov and R. Schoen,Harmonic maps into singular spaces and p-adic superrigidity for lattices in groups of rank one, preprint.Google Scholar
  8. [Jac1] N. Jacobson,Basic Algebra II, W. H. Freeman and Co., San Francisco, 1980.MATHGoogle Scholar
  9. [Joh1] F. E. A. Johnson,On the existence of irreducible discrete subgroups in isotropic Lie groups of classical type, Proceedings of the London Mathematical Society (3)56 (1988), 51–77.MATHCrossRefMathSciNetGoogle Scholar
  10. [Hir1] E. Hironaka,Polynomial periodicity for Betti numbers of covering surfaces, preprint.Google Scholar
  11. [La1] S. Lang,Algebraic Number Theory, Springer-Verlag, New York, 1986.MATHGoogle Scholar
  12. [LM1] A. Lubotzky and A. Magid,Varieties of representations of finitely generated groups, Memoirs of the American Mathematical Society58 no. 336 (1985).Google Scholar
  13. [Mar1] G. A. Margulis,Discrete Subgroups of Semisimple Lie Groups, Springer-Verlag, New York, 1991.MATHGoogle Scholar
  14. [Rag1] M. S. Raghunathan,Discrete Subgroups of Lie Groups, Ergebnisse (Band 68), Springer-Verlag, New York, 1991.Google Scholar
  15. [Rud1] Z. Rudnick,Representation varieties of solvable groups, Journal of Pure and Applied Algebra45 (1987), 261–272.MATHCrossRefMathSciNetGoogle Scholar
  16. [SarAd1] P. Sarnak and S. Adams,Betti numbers of congruence groups, Israel Journal of Mathematics, this issue, pp. 31–72.Google Scholar
  17. [Zim1] R. Zimmer,Ergodic Theory and Semisimple Groups, Birkhäuser, Boston, 1984.MATHGoogle Scholar

Copyright information

© Hebrew University 1994

Authors and Affiliations

  • Scot Adams
    • 1
  1. 1.Department of MathematicsUniversity of ChicagoChicagoUSA

Personalised recommendations