Pure Maths Colloquium: Topology of diffeomorphism groups
14 May 2007 16:15 in CM221
I will present an overview of results on the topology of groups
of diffeomorphisms of symplectic manifolds. I will talk about the
various methods and sketch the proofs of at least two results:
1. The cohomology ring of the group of symplectic diffeomorphisms
of a closed symplectic manifold is infinitely generated in many cases.
2. A Reznikov's theorem saying that the action
of SU(n+1) on CP^n induces an injection on rational homology.
Both proofs uses basic algebraic topology and a little bit of
symplectic geometry (as a black box).
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