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Summary: COHERENCE, LOCAL QUASICONVEXITY,
AND THE PERIMETER OF 2-COMPLEXES
JONATHAN P. MCCAMMOND 1
AND DANIEL T. WISE 2
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.
Contents
1. Introduction 2
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