Centralizers of Hamiltonian Circle Actions on Rational Ruled Surfaces

Pranav V. Chakravarthy, Universite Libre de Bruxelles, Belgium. Martin Pinsonnault, The University of Western Ontario, London, Ontario, Canada.

Chapters 1. Introduction 2. Hamiltonian torus actions on ruled $4$-manifolds 3. Action of $\operatorname {Symp}^{S^1}(S^{2} \times S^{2},\omega _{\lambda })$ on $\mathcal {J}^{S^1}_{\omega _{\lambda }}$ 4. The homotopy type of the symplectic centralisers of $S^1(a,b;m)$ 5. Partition of the space of invariant almost-complex structures 6. Circle actions on $\mathbb {C}P^{2}\# \overline {\mathbb {C}P^{2}}$ A. Equivariant versions of classical results from Differential Topology B. Equivariant automorphism groups C. $J$-Holomorphic configurations and equivariant Gompf argument D. Alexander-Eells isomorphism