Fundamental groups of asymptotic cones
| dc.creator | Erschler, A. G. | |
| dc.creator | Osin, D. V. | |
| dc.date | 2004-04-05 | |
| dc.date | 2005-02-26 | |
| dc.date.accessioned | 2026-07-07T05:07:11Z | |
| dc.date.available | 2026-07-07T05:07:11Z | |
| dc.description | We show that for any metric space $M$ satisfying certain natural conditions, there is a finitely generated group $G$, an ultrafilter $ω$, and an isometric embedding $ι$ of $M$ to the asymptotic cone ${\rm Cone}_ω(G)$ such that the induced homomorphism $ι^ \ast :π_1(M)\to π_1({\rm Cone}_ω(G))$ 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. | |
| dc.description | This is a corrected version of the paper. Some proofs are improved and several typos are corrected. The main result remains unchanged | |
| dc.identifier | https://arxiv.org/abs/math/0404111 | |
| dc.identifier | http://arxiv.org/abs/math/0404111 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70756 | |
| dc.subject | Group Theory | |
| dc.subject | Primary: 20F69; Secondary: 14F35, 20F06 | |
| dc.title | Fundamental groups of asymptotic cones | |
| dc.type | text |