Adding high powered relations to large groups

dc.creatorLackenby, Marc
dc.date2005-12-15
dc.date2007-03-29
dc.date.accessioned2026-07-07T07:54:55Z
dc.date.available2026-07-07T07:54:55Z
dc.descriptionA 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.description15 pages, 7 figures; v2: minor corrections and improved exposition; to appear in Mathematical Research Letters
dc.identifierhttps://arxiv.org/abs/math/0512356
dc.identifierhttp://arxiv.org/abs/math/0512356
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/126793
dc.subjectGroup Theory
dc.subjectGeometric Topology
dc.subject20F65; 57M07, 57N10
dc.titleAdding high powered relations to large groups
dc.typetext

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