arXiv subjects

Dan Staley

Publications and source records attributed to Dan Staley.

2 recordsLinked to original sources

arXiv2009

Erratic Boundary Behavior of CAT(0) Geodesics under G-equivariant Maps

We show that, given any finite dimensional, connected, compact metric space Z, there exists a group G acting geometrically on two CAT(0) spaces X and Y, a G-equivariant quasi-isometry f from X to Y, and a geodesic ray c in X, such that the closure of f(c), instersected with the boundary of Y, is homeomorphic to Z. This characterizes all homeomorphism types of "geodesic boundary images" that arise in this manner.

math.GT↗

arXiv2009

Thompson's Group F and Uniformly Finite Homology

This paper demonstrates the uniformly finite homology developed by Block and Weinberger and its relationship to amenable spaces via applications to the Cayley graph of Thompson's Group F. In particular, a certain class of subgraph of F is shown to be non-amenable. This shows that if F is amenable, these subsets (which include every finitely generated submonoid of the positive monoid of F) must necessarily have measure zero.

math.GR↗