A generalization of the {L}yndon-{H}ochschild-{S}erre spectral sequence with applications to group cohomology and decompositions of groups
A generalization of the {L}yndon-{H}ochschild-{S}erre spectral sequence with applications to group cohomology and decompositions of groups
We set up a Grothendieck spectral sequence which generalizes the Lyndon–Hochschild–Serre spectral sequence for a group extension K ? G ? Q by allowing the normal subgroup K to be replaced by a subgroup, or family of subgroups which satisfy a weaker condition than normality. This is applied to establish a decomposition theorem for certain groups as fundamental groups of graphs of Poincaré duality groups. We further illustrate the method by proving a cohomological vanishing theorem which applies for example to Thompson's group F.
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Kropholler, P.H.
0a2b4a66-9f0d-4c52-8541-3e4b2214b9f4
May 2006
Kropholler, P.H.
0a2b4a66-9f0d-4c52-8541-3e4b2214b9f4
Kropholler, P.H.
(2006)
A generalization of the {L}yndon-{H}ochschild-{S}erre spectral sequence with applications to group cohomology and decompositions of groups.
Journal of Group Theory, 9 (1), .
(doi:10.1515/JGT.2006.001).
Abstract
We set up a Grothendieck spectral sequence which generalizes the Lyndon–Hochschild–Serre spectral sequence for a group extension K ? G ? Q by allowing the normal subgroup K to be replaced by a subgroup, or family of subgroups which satisfy a weaker condition than normality. This is applied to establish a decomposition theorem for certain groups as fundamental groups of graphs of Poincaré duality groups. We further illustrate the method by proving a cohomological vanishing theorem which applies for example to Thompson's group F.
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Published date: May 2006
Organisations:
Mathematical Sciences
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Local EPrints ID: 349590
URI: http://eprints.soton.ac.uk/id/eprint/349590
ISSN: 1433-5883
PURE UUID: 7b8336da-b317-4667-9d9f-fd8caf76ebf3
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Date deposited: 11 Mar 2013 14:11
Last modified: 15 Mar 2024 03:46
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