The University of Southampton
University of Southampton Institutional Repository

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
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.

1433-5883
1-25
Kropholler, P.H.
0a2b4a66-9f0d-4c52-8541-3e4b2214b9f4
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), 1-25. (doi:10.1515/JGT.2006.001).

Record type: Article

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.

This record has no associated files available for download.

More information

Published date: May 2006
Organisations: Mathematical Sciences

Identifiers

Local EPrints ID: 349590
URI: http://eprints.soton.ac.uk/id/eprint/349590
ISSN: 1433-5883
PURE UUID: 7b8336da-b317-4667-9d9f-fd8caf76ebf3
ORCID for P.H. Kropholler: ORCID iD orcid.org/0000-0001-5460-1512

Catalogue record

Date deposited: 11 Mar 2013 14:11
Last modified: 15 Mar 2024 03:46

Export record

Altmetrics

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×