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math.GR2005★ 1 cited
A generalization of the Lyndon--Hochschild--Serre spectral sequence with applications to group cohomology and decompositions of groups
P. H. Kropholler
We set up a Grothendieck spectral sequence which generalizes the Lyndon--Hochschild--Serre spectral sequence for a group extension $K\mono G\epi Q$ by allowing the normal subgroup…
math.GR2004★ 8 cited
Groups of small homological dimension and the Atiyah Conjecture
Peter Kropholler, Peter Linnell, Wolfgang Lueck
A group G has homological dimension less or equal to 1 if it is locally free. We prove the converse provided that G satisfies the Atiyah Conjecture about L^2-Betti numbers. We also…
math.GR2003
Invariant rings of orthogonal groups over the field of two elements
P. H. Kropholler, S. Mosheni Rajaei, J. Segal
We determine the rings of invariants in the symmetric algebra on the dual of a vector space V over the field of two elements, for the group G of orthogonal transformations preservi…