Mathematics

By a result of Kedra and Pinsonnault, we know that the topology of groupsof symplectomorphisms of symplectic 4-manifolds is complicated in general, although,in most of all known examples, the rational cohomology rings of these groups are finitelygenerated. In this talk we compute the homotopy Lie algebra of groups of symplectomorphismsof some 3-point and 4-point blow-ups of the projective plane and show it is infinite dimensional.Nevertheless, the full topology of these groups can be understood: we show it is determined bycompact subgroups arising from Hamiltonian group actions. We also discuss some applicationsto more blow-ups. Part of this work is joint with Martin Pinsonnault and Sinan Eden.