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.
Amenable groups of finite cohomological dimension and the zero divisor conjecture
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abstract
We prove that every amenable group of cohomological dimension two whose integral group ring is a domain is solvable and investigate certain homological finiteness properties of groups that satisfy the analytic zero divisor conjecture and act on an acyclic CW-complex with amenable stabilisers.
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2019 1verdicts
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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.