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Proceedings of the American Mathematical Society

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Rigidity of trivial actions of abelian-by-cyclic groups


Author: Anne E. McCarthy
Journal: Proc. Amer. Math. Soc. 138 (2010), 1395-1403
MSC (2000): Primary 37-XX
Published electronically: November 10, 2009
MathSciNet review: 2578531
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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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Additional Information

Anne E. McCarthy
Affiliation: Department of Mathematics, Fort Lewis College, Durango, Colorado 81301

DOI: https://doi.org/10.1090/S0002-9939-09-10173-9
Received by editor(s): January 29, 2009
Received by editor(s) in revised form: August 4, 2009
Published electronically: November 10, 2009
Communicated by: Jane M. Hawkins
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.