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arXiv · 1506.03233

Recognizing a relatively hyperbolic group by its Dehn fillings

François Dahmani·Vincent Guirardel
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Abstract

Dehn fillings for relatively hyperbolic groups generalize the topological Dehn surgery on a non-compact hyperbolic $3$-manifold such as a hyperbolic knot complement. We prove a rigidity result saying that if two non-elementary relatively hyperbolic groups without suitable 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 non-elementary relatively hyperbolic groups with residually finite parabolic groups and with no suitable splittings.

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BibTeXRIS

François Dahmani, Vincent Guirardel. 2018-04-18. Recognizing a relatively hyperbolic group by its Dehn fillings. https://doi.org/10.1215/00127094-2018-0014

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