Expanders, rank and graphs of groups
| dc.creator | Lackenby, Marc | |
| dc.date | 2004-03-08 | |
| dc.date | 2005-04-01 | |
| dc.date.accessioned | 2026-07-07T05:06:11Z | |
| dc.date.available | 2026-07-07T05:06:11Z | |
| dc.description | Let G be a finitely presented group, and let {G_i} be a collection of finite index normal subgroups that is closed under intersections. Then, we prove that at least one of the following must hold: 1. G_i is an amalgamated free product or HNN extension, for infinitely many i; 2. the Cayley graphs of G/G_i (with respect to a fixed finite set of generators for G) form an expanding family; 3. inf_i (d(G_i)-1)/[G:G_i] = 0, where d(G_i) is the rank of G_i. The proof involves an analysis of the geometry and topology of finite Cayley graphs. Several applications of this result are given. | |
| dc.description | 13 pages; to appear in Israel J. Math | |
| dc.identifier | https://arxiv.org/abs/math/0403127 | |
| dc.identifier | http://arxiv.org/abs/math/0403127 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70383 | |
| dc.subject | Group Theory | |
| dc.subject | Geometric Topology | |
| dc.subject | 20F65; 20E06, 20F05, 05C25 | |
| dc.title | Expanders, rank and graphs of groups | |
| dc.type | text |