Detecting geometric splittings in finitely presented groups
Abstract
We present an algorithm which given a presentation of a group without 2-torsion, a solution to the word problem with respect to this presentation, and an acylindricity constant , outputs a collection of tracks in an appropriate presentation complex. We give two applications: the first is an algorithm which decides if admits an essential free decomposition, the second is an algorithm which; if is relatively hyperbolic; decides if it admits an essential elementary splitting.
Cite
@article{arxiv.0906.3902,
title = {Detecting geometric splittings in finitely presented groups},
author = {Nicholas W. M. Touikan},
journal= {arXiv preprint arXiv:0906.3902},
year = {2018}
}
Comments
This is a rewritten version of the paper "Finding tracks in 2-complexes". The statements of the main theorems are unchanged and the proof is essentially the same, but the presentation has been substantially improved. To appear in Transactions of the American Mathematical Society