Rigidity of trivial actions of abelian-by-cyclic groups

McCarthy, Anne

doi:10.1090/S0002-9939-09-10173-9

Rigidity of trivial actions of abelian-by-cyclic groups
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by Anne E. McCarthy PDF

Proc. Amer. Math. Soc. 138 (2010), 1395-1403 Request permission

Abstract:

Let $\Gamma _A$ denote the abelian-by-cyclic group associated to an integer-valued, non-singular matrix $A$. We show that if $A$ has no eigenvalues of modulus one, then there are no faithful $C^1$ perturbations of the trivial action $\iota : \Gamma _A \to \mathrm {Diff}^1(M)$, where $M$ is a compact manifold.

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