Detecting geometric splittings in finitely presented groups
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- by Nicholas W. M. Touikan PDF
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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.References
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Additional Information
- Nicholas W. M. Touikan
- Affiliation: Department of Mathematical Sciences, Stevens Institute of Technology, Hoboken, New Jersey 07030
- MR Author ID: 803915
- Email: nicholas.touikan@gmail.com
- 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
- © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 370 (2018), 5635-5704
- MSC (2010): Primary 20E06, 20F10; Secondary 57M05, 20E08
- DOI: https://doi.org/10.1090/tran/7152
- MathSciNet review: 3803145