A spectral sequence for Dehn fillings

Abstract

We study how the cohomology of a type $F_{\infty }$ relatively hyperbolic group pair $(G,\mathcal{P})$ changes under Dehn fillings (i.e. quotients of group pairs). For sufficiently long Dehn fillings where the quotient pair $(\bar{G},\bar{\mathcal{P}})$ is of type $F_{\infty }$, we show that there is a spectral sequence relating the cohomology groups $H^i(G,\mathcal{P};\mathbb{Z}G)$ and $H^i\left(\bar{G},\bar{\mathcal{P}};\mathbb{Z}\bar{G}\right)$. As a consequence, we show that essential cohomological dimension does not increase under these Dehn fillings.

arXiv commentAccepted version

References in corpus (5)

• Relative hyperbolicity and relative quasiconvexity for countable groups
• Hyperbolically embedded subgroups and rotating families in groups acting on hyperbolic spaces
• Peripheral fillings of relatively hyperbolic groups
• Cohomology of group theoretic Dehn fillings I: Cohen-Lyndon type theorems
• Boundaries of Dehn fillings

Cited by in corpus (2)

• Cohomology of group theoretic Dehn fillings II
• Cohomology of group theoretic Dehn fillings II: A spectral sequence