Almost isometric actions, property (T), and local rigidity
By D. Fisher, Gregory Margulis. 2003
77 citations recorded by the source corpus.
Let Γ be a discrete group with property (T) of Kazhdan. We prove that any Riemannian isometric action of Γ 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 [FM2].One definition of property (T) is that a group Γ has property (T) if every isometric Γ 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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/083c91fee54db67a2e31df484a1a54b906e2c3b3
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- On limits of finite graphs (2005, background): “ive measure µ, where µ([{Si}∞ i=1]) = lim ω µi(Si). Notice that [{Si}∞ i=1] stands for the equivalence class of the element {Si} ∞ i=1 ∈ Q∞ i=1 B(Qi). The Boolean algebra UQ is complete (see e.g [2], [4]). The measure algebra we obtain is not separable, it is called the Loeb measure algebra. Note th”
- A new proof of Gromov's theorem on groups of polynomial growth (2007, result): “The following theorem is a very weak version of some results in [ FM05 ], see also [Gro03, pp.115-116]:”
- Property (T) and rigidity for actions on Banach spaces (2005, background): “One of the motivations to consider such questions came from the work of Fisher and Margulis [ FM1 ], [FM2], in which an Lp analogue of property (T) with p 2”
- Groups acting on manifolds: around the Zimmer program (2008, result): “A result noticed by the author and Margulis and contained in a paper of Bader, Furman, Gelander, and Monod allows one to adapt this proof for values of k slightly less than 3 2 [5, 81].”