Volume 21, issue 5 (2021)

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A spectral sequence for Dehn fillings

Oliver H Wang

Algebraic & Geometric Topology 21 (2021) 2257–2272
Abstract

We study how the cohomology of a type F relatively hyperbolic group pair (G,𝒫) changes under Dehn fillings (ie quotients of group pairs). For sufficiently long Dehn fillings where the quotient pair (,𝒫̄) is of type F, we show that there is a spectral sequence relating the cohomology groups Hi(G,𝒫; G) and Hi(,𝒫̄; ). As a consequence, we show that essential cohomological dimension does not increase under these Dehn fillings.

Keywords
relatively hyperbolic group, Bowditch boundary, group cohomology, Dehn filling, spectral sequence
Mathematical Subject Classification 2010
Primary: 20J06
Secondary: 20F65
References
Publication
Received: 30 July 2018
Revised: 5 September 2020
Accepted: 3 December 2020
Published: 31 October 2021
Authors
Oliver H Wang
Department of Mathematics
The University of Chicago
Chicago, IL
United States
http://math.uchicago.edu/~oliver/