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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
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/40590731
Page Count: 9
You can always find the topics here!Topics: Matrices, Mathematical manifolds, Mathematical triviality, Mathematical theorems, Topological theorems, Eigenvalues, Mathematical surfaces, Homomorphisms, Mathematical vectors
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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.
Proceedings of the American Mathematical Society © 2010 American Mathematical Society