Cat ( 0 )
نویسندگان
چکیده
منابع مشابه
On Splitting Theorems for Cat(0) Spaces and Compact Geodesic Spaces of Non-positive Curvature
In this paper, we prove some splitting theorems for CAT(0) spaces on which some product group acts geometrically and show a splitting theorem for compact geodesic spaces of nonpositive curvature. A CAT(0) group Γ is said to be rigid, if Γ determines the boundary up to homeomorphism of a CAT(0) space on which Γ acts geometrically. Croke and Kleiner have constructed a non-rigid CAT(0) group. As a...
متن کاملCusped hyperbolic 3-manifolds: canonically CAT(0) with CAT(0) spines
We prove that every finite-volume hyperbolic 3-manifold M with p ≥ 1 cusps admits a canonical, complete, piecewise Euclidean CAT(0) metric, with a canonical projection to a CAT(0) spine K∗ M . Moreover: (a) The universal cover of M endowed with the CAT(0) metric is a union of Euclidean half-spaces, glued together by identifying Euclidean polygons in their bounding planes by pairwise isometry; (...
متن کاملAsymptotically CAT(0) Groups
We develop a general theory for asymptotically CAT(0) groups; these are groups acting geometrically on a geodesic space, all of whose asymptotic cones are CAT(0).
متن کاملCat(0) Groups and Coxeter Groups Whose Boundaries Are Scrambled Sets
In this paper, we study CAT(0) groups and Coxeter groups whose boundaries are scrambled sets. Suppose that a group G acts geometrically (i.e. properly and cocompactly by isometries) on a CAT(0) space X. (Such group G is called a CAT(0) group.) Then the group G acts by homeomorphisms on the boundary ∂X of X and we can define a metric d∂X on the boundary ∂X. The boundary ∂X is called a scrambled ...
متن کاملHomotopy of Ends and Boundaries of CAT(0) Groups
For n ≥ 0, we exhibit CAT(0) groups that are n-connected at infinity, and have boundary which is (n− 1)-connected, but this boundary has non-trivial n-homotopy group. In particular, we construct 1ended CAT(0) groups that are simply connected at infinity, but have a boundary with non-trivial fundamental group. Our base examples are 1-ended CAT(0) groups that have non-path connected boundaries. I...
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
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