The geometry of surface-by-free groups
| dc.creator | Farb, Benson | |
| dc.creator | Mosher, Lee | |
| dc.date | 2000-08-29 | |
| dc.date.accessioned | 2026-07-07T04:37:02Z | |
| dc.date.available | 2026-07-07T04:37:02Z | |
| dc.description | We show that every word hyperbolic, surface-by-(noncyclic) free group Gamma is as rigid as possible: the quasi-isometry group of Gamma equals the abstract commensurator group Comm(Gamma), which in turn contains Gamma as a finite index subgroup. As a corollary, two such groups are quasi-isometric if and only if they are commensurable, and any finitely generated group quasi-isometric to Gamma must be weakly commensurable with Gamma. We use quasi-isometries to compute Comm(Gamma) explicitly, an example of how quasi-isometries can actually detect finite index information. The proofs of these theorems involve ideas from coarse topology, Teichmuller geometry, pseudo-Anosov dynamics, and singular solv-geometry. | |
| dc.description | 48 pages | |
| dc.identifier | https://arxiv.org/abs/math/0008215 | |
| dc.identifier | http://arxiv.org/abs/math/0008215 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59813 | |
| dc.subject | Group Theory | |
| dc.subject | 20F65; 20F67 | |
| dc.title | The geometry of surface-by-free groups | |
| dc.type | text |