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- W2951506190 abstract "Let $Gamma$ be a discrete group with property $(T)$ of Kazhdan. We prove that any Riemannian isometric action of $Gamma$ on a compact manifold $X$ is locally rigid. We also prove a more general foliated version of this result. The foliated result is used in our proof of local rigidity for standard actions of higher rank semisimple Lie groups and their lattices in cite{FM2}. One definition of property $(T)$ is that a group $Gamma$ has property $(T)$ if every isometric $Gamma$ action on a Hilbert space has a fixed point. We prove a variety of strengthenings of this fixed point properties for groups with property $(T)$. Some of these are used in the proofs of our local rigidity theorems." @default.
- W2951506190 created "2019-06-27" @default.
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- W2951506190 date "2003-12-19" @default.
- W2951506190 modified "2023-09-27" @default.
- W2951506190 title "Almost isometric actions, property $(T)$, and local rigidity" @default.
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