%0 Journal Article
%T Finding tracks in 2-complexes
%A Nicholas W. M. Touikan
%J Mathematics
%D 2009
%I arXiv
%X We present an algorithm which given a presentation of a group G without 2-torsion, a solution to the word problem with respect to this presentation, and an acylindricity constant {\kappa}, outputs a collection of tracks in an appropriate presentation complex. We give two applications: the first is an algorithm which decides if G admits an essential free decomposition, the second is an algorithm which; if G is relatively hyperbolic; decides if it admits an essential elementary splitting.
%U http://arxiv.org/abs/0906.3902v2