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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