Local rigidity for certain groups of toral automorphisms

Anatoly Katok, J. Lewis

Research output: Contribution to journalArticle

54 Citations (Scopus)

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

Fingerprint

Rigidity
Automorphisms
Subgroup
Maximal Rank
Diffeomorphism
Diffeomorphisms
Theorem
Standards

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Katok, Anatoly ; Lewis, J. / Local rigidity for certain groups of toral automorphisms. In: Israel Journal of Mathematics. 1991 ; Vol. 75, No. 2-3. pp. 203-241.
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Local rigidity for certain groups of toral automorphisms. / Katok, Anatoly; Lewis, J.

In: Israel Journal of Mathematics, Vol. 75, No. 2-3, 01.10.1991, p. 203-241.

Research output: Contribution to journalArticle

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