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Boundaries of Dehn fillings

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arxiv 1612.03497 v2 pith:UHGPWAC4 submitted 2016-12-11 math.GR

Daniel Groves , Jason Fox Manning , Alessandro Sisto This is my paper · ORCID
classification math.GR
keywords dehnhyperbolicboundariesboundarycannonconjecturefillingsrelatively
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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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  1. Cohomology of group theoretic Dehn fillings II

    math.GR 2019-08 accept novelty 7.0 of 10

    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 acylind...

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