Jerusalem Mathematics Colloquium

Thursday, 4th January 2007, 4:00 pm
Mathematics Building, Lecture Hall 2

Assaf Libman
(University of Aberdeen)

"Orbit spaces and decompositions of classifying spaces"

Abstract: Given two G-spaces (G a compact Lie group), when are their orbit spaces homotopy equivalent? I will discuss a new and surprisingly elementary method which guarantees such an equivalence. This result gives a quick and elegant proof of Webb's conjecture, namely to the contractibility of the orbit space of the simplicial complex associated to the non-trivial p-subgroups of a finite group G. This conjecture has been proved by Peter Symonds, but his method does not extended to compact Lie groups, unlike the approach I will present.

The ideas can also be used to determine when a map between two G-spaces induces an isomorphism in equivariant cohomology. There results a direct sum decomposition of the cohomology ring of a finite group G, known as Webb's formula. This decomposition is a shadow of a stronger topological result on the classifying space of G. Our methods have the advantage that they extend without difficulty to compact Lie groups.

Light refreshments will be served in the faculty lounge at 3:30.

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