Consider a compact symplectic manifold of dimension $2n$ which is acted on by a circle in a Hamiltonian way with isolated fixed points; we refer to it as a Hamiltonian $S^1$-space. In [S] it is proved that the minimal Chern number $N$ is bounded above by $n+1$, bound which is expected for all positive monotone compact symplectic manifolds. Assuming that the Hamiltonian $S^1$-space is monotone (i.e. the first Chern class is a multiple of the class of the symplectic form) in [GHS] several bounds on the Betti numbers are proved, these bounds depending on N. I will first discuss the ideas behind the proofs of the aforementioned facts, and then concentrate on $N=n+1$. In this case my student Isabelle Charton [C] proved that the manifold must be homotopically equivalent to a complex projective space of dimension $2n$.
Mittwoch, den 6. Februar 2019 um 16.00 Uhr, in Mathematicon, INF 205, SR 4 Mittwoch, den 6. Februar 2019 at 16.00, in Mathematicon, INF 205, SR 4
Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. Peter Albers