Coherence, local quasiconvexity, and the perimeter of 2-complexes
By Jon McCammond, Daniel T. Wise. 2002
48 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/62fc0d95d6e451c612bc93711e49fdc9bb9cd100
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Geometry and Topology
- Daniel T. Wise
- Ilya Kapovich
- Paul E. Schupp
- Jon McCammond
- Frédéric Haglund
- Mark F. Hagen
- Yann Ollivier
- Denis V. Osin
In Mathematical Physics
- Ilya Kapovich
- Paul E. Schupp
- Daniel T. Wise
- Jon McCammond
- Mark F. Hagen
- Yann Ollivier
- Frédéric Haglund
- Anthony Genevois
Citations in the corpus
- Fans and Ladders in Small Cancellation Theory (2002, methodology): “While the coherence proofs in [14] already work in conjunction with traditional small cancellation theory, the method applies to a signi®cantly larger class of groups when combined with the results of this paper asserting the existence of fans.”
- Genericity, the Arzhantseva-Ol’shanskii method and the isomorphism problem for one-relator groups (2002, methodology): “hat this method is applicable in a variety of situations and deserves to be much more widely known and used. Their method is in many ways dual to the “perimeter reduction” technique of McCammond-Wise [8, 29, 42, 55]. Both methods allow one to study subgroups of non-free groups by means of Stallings ”