Gerasim Kokarev (University of Edinburgh)
g.kokarev@ed.ac.uk Due to Gottlieb's application of Nielsen-Wecken fixed point classes, the evaluation map from a diffeomorphism group Diff(M) is contractible on the 1-skeleton provided the Euler-Poincaré number of M does not vanish. I will tell about similar results on the contractibility of the evaluation map on certain 2-cycles in Diff(M) for a closed symplectic manifold M. More precisely, I will describe the relationship between obstructions for analogous vanishing theorems and the presence of rational curves.