Local rigidity for certain groups of toral automorphisms

Anatoly Katok, J. Lewis

Research output: Contribution to journalArticlepeer-review

59 Scopus citations

Abstract

Let Γ = SL(n, ℤ) or any subgroup of finite index, n ≥ 4. We show that the standard action of Γ on {Mathematical expression} n is locally rigid, i.e., every action of Γ on {Mathematical expression} n by C diffeomorphisms which is sufficiently close to the standard action is conjugate to the standard action by a C diffeomorphism. In the course of the proof, we obtain a global rigidity result (Theorem 4.12) for actions of free abelian subgroups of maximal rank in SL(n, ℤ).

Original languageEnglish (US)
Pages (from-to)203-241
Number of pages39
JournalIsrael Journal of Mathematics
Volume75
Issue number2-3
DOIs
StatePublished - Oct 1 1991

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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