School of Mathematics Seminars and Lectures

Homotopy type of equivariant symplectomorphisms of rational ruled surfaces

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

Wednesday, September 21, 2022 from to (Asia/Kolkata)
at 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.