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Transactions of the American Mathematical Society

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Detecting geometric splittings in finitely presented groups


Author: Nicholas W. M. Touikan
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 20E06, 20F10; Secondary 57M05, 20E08
DOI: https://doi.org/10.1090/tran/7152
Published electronically: March 22, 2018
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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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Additional Information

Nicholas W. M. Touikan
Affiliation: Department of Mathematical Sciences, Stevens Institute of Technology, Hoboken, New Jersey 07030
Email: nicholas.touikan@gmail.com

DOI: https://doi.org/10.1090/tran/7152
Received by editor(s): March 8, 2011
Received by editor(s) in revised form: June 18, 2015, August 17, 2016, and December 10, 2016
Published electronically: March 22, 2018
Article copyright: © Copyright 2018 American Mathematical Society

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