Adding high powered relations to large groups

Details Adding high powered relations to large groups Adding high powered relations to large groups

2005-12-15

arxiv.org/abs/math/0512356v2

Mathematics

Group Theory

15 pages, 7 figures; v2: minor corrections and improved exposition; to appear in Mathematical Research Letters

Scientific paper

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/<> 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.

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