Nikon Kurnosov (Moscow) will speak in the geometry seminar on 10th November. The talk will be at 2pm in O8.08, 8th floor of building NO. Nikon’s title is Betti numbers of hyperkahler manifolds and his abstract follows.
Let M be a simple hyperkahler manifold, that is, a compact Riemannian manifold with holonomy equal to Sp(n). There are two known families of such manifolds and two sporadic examples; the quest to find more (or to prove that none other exist) is still ongoing. It is known that there are only finitely many families with a given second cohomology lattice, hence the bounds on second Betti number provide restrictions on the number of deformation classes of hyperkahler manifolds. I will explain boundary conditions for the second Betti number which follow from Rozansky-Witten invariants and so(4, b_2-2)-action on cohomology.