Homotopy of Ends and Boundaries of CAT(0) Groups
نویسندگان
چکیده
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. In particular, we show all parabolic semidirect products of the free group of rank 2 and Z have a non-path connected boundary.
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 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 کاملVibration Analysis of a Nonlinear Beam Under Axial Force by Homotopy Analysis Method
In this paper, Homotopy Analysis Method is used to analyze free non-linear vibrations of a beam simply supported by pinned ends under axial force. Mid-plane stretching is also considered for dynamic equation extracted for the beam. Galerkin decomposition technique is used to transform a partial dimensionless nonlinear differential equation of dynamic motion into an ordinary nonlinear differenti...
متن کاملSpaces with Finitely Many Non-trivial Homotopy Groups
It is well known that the homotopy category of connected CW-complexes X whose homotopy groups n;(X) are trivial for i> 1 is equivalent to the category of groups. One of the objects of this paper is to prove a similar equivalence for the connected CW-complexes X whose homotopy groups are trivial for i > n + 1 (where n is a fixed non-negative integer). For n = 1 the notion of crossed module inven...
متن کاملHOMOTOPY PERTURBATION METHOD FOR SOLVING FLOW IN THE EXTRUSION PROCESSES
In this paper, the homotopy perturbation method (HPM) is considered for finding approximate solutions of two-dimensional viscous flow. This technique provides a sequence of functions which converges to the exact solution of the problem. The HPM does not need a small parameters in the equations, but; the perturbation method depends on small parameter assumption and the obtained results. In most ...
متن کامل