Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9516291 | Topology | 2005 | 17 Pages |
Abstract
We show that for any metric space M satisfying certain natural conditions, there is a finitely generated group G, an ultrafilter Ï, and an isometric embedding ι of M to the asymptotic cone ConeÏ(G) such that the induced homomorphism ι*:Ï1(M)âÏ1(ConeÏ(G)) is injective. In particular, we prove that any countable group can be embedded into a fundamental group of an asymptotic cone of a finitely generated group.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
A. Erschler, D. Osin,