Geodesic flow for CAT.0/–groups
نویسندگان
چکیده
In Bartels–Lück [1] we introduced the concept of transfer reducible groups with respect to a family of subgroups. This definition is somewhat technical and recalled as Definition 0.4 below. We showed that groups that are transfer reducible over the family of virtually cyclic subgroups satisfy the Farrell–Jones Conjecture with coefficients in an additive category. For further explanations about the Farrell–Jones Conjecture we refer for instance to [1], Bartels–Lück–Reich [3] and Lück–Reich [8], where more information about the applications, history, literature and status is given.
منابع مشابه
Asymptotically 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 کاملThe Weak Specification Property for Geodesic Flows on Cat(-1) Spaces
We prove that the geodesic flow on a compact locally CAT(−1) space has the weak specification property, and give various applications of this property. We show that every Hölder continuous function on the space of geodesics has a unique equilibrium state, and as a result, that the BowenMargulis measure is the unique measure of maximal entropy. We establish the equidistribution of weighted perio...
متن کاملFlat strips, Bowen-Margulis measures, and mixing of the geodesic flow for rank one CAT(0) spaces
Let X be a proper, geodesically complete CAT(0) space under a proper, non-elementary, isometric action by a group Γ with a rank one element. We construct a generalized Bowen-Margulis measure on the space of unit-speed parametrized geodesics of X modulo the Γ-action. Although the construction of Bowen-Margulis measures for rank one nonpositively curved manifolds and for CAT(−1) spaces is well-kn...
متن کاملOn 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 کاملCocompact Proper CAT(0) Spaces
This paper is about geometric and topological properties of a proper CAT(0) spaceX which is cocompact i.e. which has a compact generating domain with respect to the full isometry group. It is shown that geodesic segments in X can “almost” be extended to geodesic rays. A basic ingredient of the proof of this geometric statement is the topological theorem that there is a top dimension d in which ...
متن کاملErgodicity of Bowen-margulis Measure for the Benoist 3-manifolds: Extended Version
We study the geodesic flow of a class of 3-manifolds introduced by Benoist which have some hyperbolicity but are non-Riemannian, not CAT(0), and with non-C geodesic flow. The geometries are nonstrictly convex Hilbert geometries in dimension three which admit compact quotient manifolds by discrete groups of projective transformations. We prove the Patterson-Sullivan density is canonical, with ap...
متن کامل