1 September 2018 Recognizing a relatively hyperbolic group by its Dehn fillings
François Dahmani, Vincent Guirardel
Duke Math. J. 167(12): 2189-2241 (1 September 2018). DOI: 10.1215/00127094-2018-0014

Abstract

Dehn fillings for relatively hyperbolic groups generalize the topological Dehn surgery on a noncompact hyperbolic 3-manifold such as hyperbolic knot complements. We prove a rigidity result saying that if two nonelementary relatively hyperbolic groups without certain splittings have sufficiently many isomorphic Dehn fillings, then these groups are in fact isomorphic. Our main application is a solution to the isomorphism problem in the class of nonelementary relatively hyperbolic groups with residually finite parabolic groups and with no suitable splittings.

Citation

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François Dahmani. Vincent Guirardel. "Recognizing a relatively hyperbolic group by its Dehn fillings." Duke Math. J. 167 (12) 2189 - 2241, 1 September 2018. https://doi.org/10.1215/00127094-2018-0014

Information

Received: 24 January 2017; Revised: 1 March 2018; Published: 1 September 2018
First available in Project Euclid: 20 July 2018

zbMATH: 06966871
MathSciNet: MR3848390
Digital Object Identifier: 10.1215/00127094-2018-0014

Subjects:
Primary: 20F65
Secondary: 20F67

Keywords: Dehn filling , isomorphism problem , relatively hyperbolic group

Rights: Copyright © 2018 Duke University Press

Vol.167 • No. 12 • 1 September 2018
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