منابع مشابه
Groups Acting on CAT (0) Square Complexes
We study groups acting on CAT (0) square complexes. In particular we show if Y is a nonpositively curved (in the sense of A. D. Alexandrov) finite square complex and the vertex links of Y contain no simple loop consisting of five edges, then any subgroup of π1(Y ) either is virtually free abelian or contains a free group of rank two. In addition we discuss when a group generated by two hyperbol...
متن کاملGroups acting on CAT(0) cube complexes
We show that groups satisfying Kazhdan’s property (T) have no unbounded actions on nite dimensional CAT(0) cube complexes, and deduce that there is a locally CAT(−1) Riemannian manifold which is not homotopy equivalent to any nite dimensional, locally CAT(0) cube complex. AMS Classi cation numbers Primary: 20F32 Secondary: 20E42, 20G20
متن کاملNon-hyperbolic automatic groups and groups acting on CAT(0) cube complexes
This note is a brief summary of my talk that I gave at RIMS workshop “Complex Analysis and Topology of Discrete Groups and Hyperbolic Spaces.” See [4] for detail. If a group G has a finite K(G, 1) and does not contain any Baumslag–Solitar groups, is G hyperbolic? (See [1].) This is one of the most famous questions on hyperbolic groups. Probably, many people expect that the answer is negative, a...
متن کاملProduct 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...
متن کاملGroups Not Acting on Manifolds
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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ژورنال
عنوان ژورنال: Geometriae Dedicata
سال: 2004
ISSN: 0046-5755,1572-9168
DOI: 10.1007/s10711-004-1527-7