منابع مشابه
Product Groups Acting on Manifolds
We analyse volume-preserving actions of product groups on Riemannian manifolds. To this end, we establish a new superrigidity theorem for ergodic cocycles of product groups ranging in linear groups. There are no a priori assumptions on the acting groups, except a spectral gap assumption on their action. Our main application to manifolds concerns irreducible actions of Kazhdan product groups. We...
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In this article we collect a series of observations that constrain actions of many groups on compact manifolds. In particular, we show that “generic” finitely generated groups have no smooth volume preserving actions on compact manifolds.
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In this note we announce results concerning the volume preserving actions of arithmetic subgroups of higher rank semisimple groups on compact manifolds. Our results can be considered as the first rigidity results for homomorphisms of these groups into diffeomorphism groups and show a sharp contrast between the behavior of actions of these groups and actions of free groups. Let G be a connected ...
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We prove that a finite group which admits a faithful, smooth, orientationpreserving action on an acyclic 3or 4-manifold is isomorphic to a subgroup of the orthogonal group SO(3) or SO(4), respectively. Also, the only finite nonabelian simple groups admitting a faithful, smooth action on an acyclic 5-manifold are the alternating groups A5 and A6, and from this we deduce a list of finite groups, ...
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This paper is a survey on the Zimmer program. In its broadest form, this program seeks an understanding of actions of large groups on compact manifolds. The goals of this survey are (1) to put in context the original questions and conjectures of Zimmer and Gromov that motivated the program, (2) to indicate the current state of the art on as many of these conjectures and questions as possible an...
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ژورنال
عنوان ژورنال: Duke Mathematical Journal
سال: 2009
ISSN: 0012-7094
DOI: 10.1215/00127094-2009-018