Coherence, local quasiconvexity, and the perimeter of 2-complexes |
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Authors: | J P McCammond D T Wise |
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Institution: | (1) Dept. of Math., University of California, Santa Barbara, CA 93106, USA;(2) Dept. of Math., McGill University, Montreal, Quebec, Canada, H3A 2K6 |
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Abstract: | A group is coherent if all its finitely generated subgroups are finitely presented. In this article we provide a criterion
for positively determining the coherence of a group. This criterion is based upon the notion of the perimeter of a map between
two finite 2-complexes which is introduced here. In the groups to which this theory applies, a presentation for a finitely
generated subgroup can be computed in quadratic time relative to the sum of the lengths of the generators. For many of these
groups we can show in addition that they are locally quasiconvex.
As an application of these results we prove that one-relator groups with sufficient torsion are coherent and locally quasiconvex
and we give an alternative proof of the coherence and local quasiconvexity of certain 3-manifold groups. The main application
is to establish the coherence and local quasiconvexity of many small cancellation groups.
Received: March 2004 Accepted: August 2004 |
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