caa a22 4500 388092491 CHVBK 20180307125255.0 cr unu---uuuuu 161130e199904 xx s 000 0 eng 10.1017/S0004972700032895 doi S0004972700032895 pii (NATIONALLICENCE)cambridge-10.1017/S0004972700032895 Brunsden Victor Department of Mathematics, Penn State Altoona, 3000 Ivyside Park, Altoona PA 16601, United States of America e-mail: vwb2@psu.edu Local rigidity and group cohomology I: Stowe's theorem for Banach manifolds [Elektronische Daten] [Victor Brunsden] 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. Copyright © Australian Mathematical Society 1999 Bulletin of the Australian Mathematical Society Cambridge University Press 59/2(1999-04), 271-295 0004-9727 59:2<271 1999 59 BAZ https://doi.org/10.1017/S0004972700032895 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0004972700032895 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Brunsden Victor Department of Mathematics, Penn State Altoona, 3000 Ivyside Park, Altoona PA 16601, United States of America e-mail: vwb2@psu.edu NATIONALLICENCE 773 0- Bulletin of the Australian Mathematical Society Cambridge University Press 59/2(1999-04), 271-295 0004-9727 59:2<271 1999 59 BAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge