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Cohomology of group theoretic Dehn fillings II

Cohomology of group theoretic Dehn fillings II
Cohomology of group theoretic Dehn fillings II
We study the cohomology of group theoretic Dehn fillings. Applying the Cohen-Lyndon property for sufficiently deep Dehn fillings of hyperbolically embedded subgroups H →h G, obtained by the second named author in [67], we derive
a spectral sequence that computes the cohomology of the corresponding Dehn filling quotients G. As an application, we establish an isomorphism between the relative cohomology of the group pair (G, H) and its sufficiently deep Dehn filling
quotient pair (G, H). This allows us to generalize the results of Fujiwara and Manning on simplicial volume of Dehn fillings of hyperbolic manifolds to Dehn fillings of Poincaré duality pairs.

We also strengthen the results of Olshanskii [58], DahmaniGuirardel-Osin [27] and Hull [42] on SQ-universality and common quotients of acylindrically hyperbolic groups by adding cohomological finiteness conditions. We apply these
results to obtain hyperbolic and acylindrically hyperbolic quotients with special properties.
Cohen-Lyndon property, Cohomological finiteness conditions, Cohomology of groups, Dehn filling, Hyperbolically embedded subgroup, Poincaré duality, Simplicial volume, SQ-universality
0001-8708
Petrosyan, Nansen
f169cfd6-aeee-4ad2-b147-0bf77dd1f9b6
Sun, Bin
260055c1-a8cb-452d-bdb1-305c50410be9
Petrosyan, Nansen
f169cfd6-aeee-4ad2-b147-0bf77dd1f9b6
Sun, Bin
260055c1-a8cb-452d-bdb1-305c50410be9

Petrosyan, Nansen and Sun, Bin (2024) Cohomology of group theoretic Dehn fillings II. Advances in Mathematics, 437, [109412]. (doi:10.1016/j.aim.2023.109412).

Record type: Article

Abstract

We study the cohomology of group theoretic Dehn fillings. Applying the Cohen-Lyndon property for sufficiently deep Dehn fillings of hyperbolically embedded subgroups H →h G, obtained by the second named author in [67], we derive
a spectral sequence that computes the cohomology of the corresponding Dehn filling quotients G. As an application, we establish an isomorphism between the relative cohomology of the group pair (G, H) and its sufficiently deep Dehn filling
quotient pair (G, H). This allows us to generalize the results of Fujiwara and Manning on simplicial volume of Dehn fillings of hyperbolic manifolds to Dehn fillings of Poincaré duality pairs.

We also strengthen the results of Olshanskii [58], DahmaniGuirardel-Osin [27] and Hull [42] on SQ-universality and common quotients of acylindrically hyperbolic groups by adding cohomological finiteness conditions. We apply these
results to obtain hyperbolic and acylindrically hyperbolic quotients with special properties.

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Accepted/In Press date: 5 November 2023
e-pub ahead of print date: 24 November 2023
Published date: February 2024
Additional Information: Publisher Copyright: © 2023 The Author(s)
Keywords: Cohen-Lyndon property, Cohomological finiteness conditions, Cohomology of groups, Dehn filling, Hyperbolically embedded subgroup, Poincaré duality, Simplicial volume, SQ-universality

Identifiers

Local EPrints ID: 446616
URI: http://eprints.soton.ac.uk/id/eprint/446616
ISSN: 0001-8708
PURE UUID: a3064fe3-6451-4574-befa-dba92c6ccccd
ORCID for Nansen Petrosyan: ORCID iD orcid.org/0000-0002-2768-5279

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Date deposited: 16 Feb 2021 17:32
Last modified: 06 Jun 2024 01:52

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Author: Bin Sun

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