Adding high powered relations to large groups
| dc.creator | Lackenby, Marc | |
| dc.date | 2005-12-15 | |
| dc.date | 2007-03-29 | |
| dc.date.accessioned | 2026-07-07T07:54:55Z | |
| dc.date.available | 2026-07-07T07:54:55Z | |
| dc.description | A group is known as `large' if some finite index subgroup admits a surjective homomorphism onto a non-abelian free group. The main theorem of the paper is as follows. Let G be a finitely generated, large group and let g_1,...,g_r be a collection of elements of G. Then G/<<g_1^n,...,g_r^n>> is also large, for infinitely many integers n. Furthermore, when G is free, this holds for all but finitely many n. These results have the following application to Dehn surgery. Let M be a compact orientable 3-manifold with boundary a torus. Suppose that the 3-manifold obtained by Dehn filling some slope on the boundary has large fundamental group. Then this is true for infinitely many filling slopes. | |
| dc.description | 15 pages, 7 figures; v2: minor corrections and improved exposition; to appear in Mathematical Research Letters | |
| dc.identifier | https://arxiv.org/abs/math/0512356 | |
| dc.identifier | http://arxiv.org/abs/math/0512356 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/126793 | |
| dc.subject | Group Theory | |
| dc.subject | Geometric Topology | |
| dc.subject | 20F65; 57M07, 57N10 | |
| dc.title | Adding high powered relations to large groups | |
| dc.type | text |