Finiteness Conditions in Group Cohomology

Martin Hamilton

Wednesday 9th January, 2008 16:00-17:00 Mathematics Building, room 214


One important finiteness condition in group theory is that of type FP infinity. This property is usually defined in terms of projective resolutions, but it can also be described as follows: A group G is said to be of type FP infinity if and only if the nth cohomology functors of G commute with filtered colimits for all n. In this talk we consider what happens when we weaken this property, and consider groups whose nth cohomology functors commute with filtered colimits for almost all n. We shall give some algebraic and topological characterisations, as well as show a connection to the group actions on spheres problem.

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