A spectral sequence for Dehn fillings

Wang, Oliver H

doi:10.2140/agt.2021.21.2257

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A spectral sequence for Dehn fillings

Oliver H Wang

Algebraic & Geometric Topology 21 (2021) 2257–2272

DOI: 10.2140/agt.2021.21.2257

Abstract

We study how the cohomology of a type $F_{\infty}$ relatively hyperbolic group pair $(G, 𝒫)$ changes under Dehn fillings (ie quotients of group pairs). For sufficiently long Dehn fillings where the quotient pair $(Ḡ, \bar{𝒫})$ is of type $F_{\infty}$ , we show that there is a spectral sequence relating the cohomology groups $H^{i} (G, 𝒫; ℤ G)$ and $H^{i} (Ḡ, \bar{𝒫}; ℤ Ḡ)$ . 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/

Volume 21, issue 5 (2021)