Homotopy type of equivariant symplectomorphisms of rational ruled surfaces

by Dr Pranav Chakravarthy (The Hebrew University of Jerusalem, Israel)

Wednesday 21 Sept 2022, 11:30 → 12:30 Asia/Kolkata

AG-77

Abstract: In this talk, we present results on the homotopy type of the group of equivariant symplectomorphisms of $S^2 \times S^2$ and $\mathbb{C}P^2$ blown up once under the presence of a Hamiltonian circle actions. We prove that the group of equivariant symplectomorphisms is homotopy equivalent to either a torus, or to the homotopy pushout of two tori depending on whether the circle action extends to a single toric action or to exactly two nonequivalent toric actions. Our results rely on J-holomorphic techniques, on Delzant’s classification of toric actions, and on Karshon’s classification of Hamiltonian circle actions on 4-manifolds. Time permitting we will explain results of a similar flavour on the homotopy type of $\mathbb{Z}_n$ equivariant symplectomorphisms for a large family of finite cyclic groups in the Hamiltonian group. This is based on joint work with Martin Pinsonnault.