Detecting geometric splittings in finitely presented groups

Touikan, Nicholas

doi:10.1090/tran/7152

Detecting geometric splittings in finitely presented groups
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by Nicholas W. M. Touikan PDF

Trans. Amer. Math. Soc. 370 (2018), 5635-5704 Request permission

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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