Abstract:

Abstract: In this talk, I will explain how we can compute the rational homotopy type of symplectomorphism groups of some four-manifolds. After explaining the general framework, I will focus on some rational symplectic four-manifolds for which the analysis can be carried through effectively using pseudo-holomorphic curves techniques and the theory of deformations of complex structures. For those manifolds, we will see that Symp is equivalent to an iterated homotopy pushout of maximal compact subgroups.