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Local rigidity and group cohomology I: Stowe's theorem for Banach manifolds

Published online by Cambridge University Press:  17 April 2009

Victor Brunsden
Victor Brunsden
Affiliation:
Department of Mathematics, Penn State Altoona, 3000 Ivyside Park, Altoona PA 16601, United States of America e-mail: vwb2@psu.edu
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Abstract

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Stowe's Theorem on the stability of the fixed points of a C2 action of a finitely generated group Γ is generalised to C1 actions of such groups on Banach manifolds. The result is then used to prove that if φ is a Cr action on a smooth, closed, manifold M satisfying H1(Γ, Dr−1(M)) = 0, then φ is locally rigid. Here, r ≥ 2 and Dk(M) is the space of Ck tangent vector fields on M. This generalises a local rigidity result of Weil for representations of a finitely generated group Γ in a Lie group.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 59 , Issue 2 , April 1999 , pp. 271 - 295
Copyright
Copyright © Australian Mathematical Society 1999

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