Abstract
Let $G$ be a compact Lie group and $X$ be a compact smooth $G$-manifold with finitely many $G$-fixed points. We show that if $X$ admits a $G$-equivariant hyperbolic diffeomorphism having a certain convergence property, there exists an open covering of $X$ indexed by the $G$-fixed points so that each open set is $G$-invariant and $G$-equivariantly diffeomorphic to the tangential $G$-representation at the corresponding $G$-fixed point. We also show that the converse is also true in case of holomorphic torus actions.
Citation
Hitoshi Yamanaka. "Equivariant hyperbolic diffeomorphisms and representation coverings." Osaka J. Math. 52 (4) 1017 - 1039, October 2015.
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