A generalization of the Lyndon-Hochschild-Serre spectral sequence with applications to group cohomology and decompositions of groups

Kropholler, P.H. (2006) A generalization of the Lyndon-Hochschild-Serre spectral sequence with applications to group cohomology and decompositions of groups. Journal of Group Theory, 9(1), pp. 1-25. (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.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Kropholler, Prof Peter
• Authors: Kropholler, P.H.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Journal of Group Theory
• ISSN: 1433-5883
• ISSN (Online): 1435-4446
• Published Online: 12 May 2006