Translator Disclaimer
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

Download Citation

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

Rights: Copyright © 2018 Duke University Press

JOURNAL ARTICLE
53 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.167 • No. 12 • 1 September 2018
Back to Top