Rigidity of trivial actions of abelian-by-cyclic groups
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- by Anne E. McCarthy PDF
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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.References
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Additional Information
- Anne E. McCarthy
- Affiliation: Department of Mathematics, Fort Lewis College, Durango, Colorado 81301
- 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
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 1395-1403
- MSC (2000): Primary 37-XX
- DOI: https://doi.org/10.1090/S0002-9939-09-10173-9
- MathSciNet review: 2578531