A new spectral sequence and an algebraic excision theorem control the cohomology of Dehn fillings of groups with hyperbolically embedded subgroups, with applications to Poincaré duality, simplicial volume, and acylindrically hyperbolic quotients.
Boundaries of Dehn fillings
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abstract
We begin an investigation into the behavior of Bowditch and Gromov boundaries under the operation of Dehn filling. In particular we show many Dehn fillings of a toral relatively hyperbolic group with 2-sphere boundary are hyperbolic with 2-sphere boundary. As an application, we show that the Cannon conjecture implies a relatively hyperbolic version of the Cannon conjecture.
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Cohomology of group theoretic Dehn fillings II
A new spectral sequence and an algebraic excision theorem control the cohomology of Dehn fillings of groups with hyperbolically embedded subgroups, with applications to Poincaré duality, simplicial volume, and acylindrically hyperbolic quotients.