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Local rigidity and group cohomology I: Stowe's theorem for Banach manifolds
| Content Provider | Scilit |
|---|---|
| Author | Brunsden, Victor |
| Copyright Year | 1999 |
| Description | Stowe's Theorem on the stability of the fixed points of a $C^{2}$ action of a finitely generated group Γ is generalised to $C^{1}$ actions of such groups on Banach manifolds. The result is then used to prove that if φ is a $C^{r}$ action on a smooth, closed, manifold M satisfying $H^{1}$(Γ, $D^{r−1}$(M)) = 0, then φ is locally rigid. Here, r ≥ 2 and $D^{k}$(M) is the space of $C^{k}$ 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. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/D7400B95CDCFC218F02A657C29C2C73D/S0004972700032895a.pdf/div-class-title-local-rigidity-and-group-cohomology-i-stowe-s-theorem-for-banach-manifolds-div.pdf |
| Ending Page | 295 |
| Page Count | 25 |
| Starting Page | 271 |
| ISSN | 00049727 |
| e-ISSN | 17551633 |
| DOI | 10.1017/s0004972700032895 |
| Journal | Bulletin of the Australian Mathematical Society |
| Issue Number | 2 |
| Volume Number | 59 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 1999-04-01 |
| Access Restriction | Open |
| Subject Keyword | Bulletin of the Australian Mathematical Society Stowe's Theorem Finitely Generated Group |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
