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RIGIDITY OF TRIVIAL ACTIONS OF ABELIAN-BY-CYCLIC GROUPS

ANNE E. MCCARTHY
Proceedings of the American Mathematical Society
Vol. 138, No. 4 (APRIL 2010), pp. 1395-1403
Stable URL: http://www.jstor.org/stable/40590731
Page Count: 9
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
RIGIDITY OF TRIVIAL ACTIONS OF ABELIAN-BY-CYCLIC GROUPS
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Abstract

Let T A denote the abelian-by-cyclic group associated to an integervalued, non-singular matrix A. We show that if A has no eigenvalues of modulus one, then there are no faithful C¹ perturbations of the trivial action l : T A → Diff¹ (M), where M is a compact manifold.

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