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arXiv · 0906.3902

Detecting geometric splittings in finitely presented groups

Nicholas W. M. Touikan
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Abstract

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.

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Nicholas W. M. Touikan. 2009-06-21. Detecting geometric splittings in finitely presented groups. https://doi.org/10.1090/tran/7152

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