The automorphism group of a compact group action
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- by W. D. Curtis PDF
- Trans. Amer. Math. Soc. 203 (1975), 45-54 Request permission
Abstract:
This paper contains results on the structure of the group, $\operatorname {Diff} _G^r(M)$, of equivariant ${C^r}$-diffeomorphisms of a free action of the compact Lie group $G$ on $M$. $\operatorname {Diff} _G^r(M)$ is shown to be a locally trivial principal bundle over a submanifold of ${\operatorname {Diff} ^r}(X),X$ the orbit manifold. The structural group of this bundle is ${E^r}(G,M)$, the set of equivariant ${C^r}$-diffeomorphisms which induce the identity on $X$. ${E^r}(G,M)$ is shown to be a submanifold of ${\operatorname {Diff} ^r}(M)$ and in fact a Banach Lie group $(r < \infty )$.References
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Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 203 (1975), 45-54
- MSC: Primary 58D05
- DOI: https://doi.org/10.1090/S0002-9947-1975-0368066-5
- MathSciNet review: 0368066