Cat(0) Groups with Specified Boundary

نویسنده

  • KIM RUANE
چکیده

We specify exactly which groups can act geometrically on CAT(0) spaces whose visual boundary is homeomorphic to either a circle or a suspension of a Cantor set.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Homotopy 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 کامل

Cat(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 کامل

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 کامل

Dense Subsets of Boundaries of Cat(0) Groups

In this paper, we study dense subsets of boundaries of CAT(0) groups. Suppose that a group G acts geometrically on a CAT(0) space X and suppose that there exists an element g0 ∈ G such that (1) Zg0 is finite, (2) X \ Fg0 is not connnected, and (3) each component of X \ Fg0 is convex and not g0-invariant, where Zg0 is the centralizer of g0 and Fg0 is the fixed-point set of g0 in X (that is, Zg0 ...

متن کامل

Cocompact 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 کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2006