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

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)271-295
Number of pages25
JournalBulletin of the Australian Mathematical Society
Volume59
Issue number2
DOIs
StatePublished - Apr 1999

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Fingerprint Dive into the research topics of 'Local rigidity and group cohomology I: Stowe's theorem for Banach manifolds'. Together they form a unique fingerprint.

Cite this