منابع مشابه
Groups 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 کاملGroups 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 کاملIsometry Groups of Cat(0) Cube Complexes
Given a CAT(0) cube complex X, we show that if Aut(X) 6= Isom(X) then there exists a full subcomplex of X which decomposes as a product with R. As applications, we prove that ifX is δ-hyperbolic, cocompact and 1-ended, then Aut(X) = Isom(X) unless X is quasi-isometric to H, and extend the rank-rigidity result of Caprace–Sageev to any lattice Γ ≤ Isom(X).
متن کاملCoxeter Groups Act on Cat(0) Cube Complexes
We show that any finitely generated Coxeter group acts properly discontinuously on a locally finite, finite dimensional CAT(0) cube complex. For any word hyperbolic or right angled Coxeter group we prove that the cubing is cocompact. We show how the local structure of the cubing is related to the partial order studied by Brink and Howlett in their proof of automaticity for Coxeter groups. In hi...
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ژورنال
عنوان ژورنال: Geometry & Topology
سال: 1997
ISSN: 1364-0380,1465-3060
DOI: 10.2140/gt.1997.1.1