Symplectic structure and almost complex structure on instanton moduli spaces
Time: 2022-03-28
Published By: Yu Feng
Speaker(s): Shuaige Qiao(BICMR)
Time: 10:00-11:30 April 1, 2022
Venue: Room 29, Quan Zhai, BICMR
Given a closed oriented Riemannian 4-manifold X and an SU(2)-principal bundle P over X, Yang-Mills equations defines an instanton moduli space, through which we could define Donaldson invariants. In this talk, I will introduce an approach to define almost complex structure or symplectic structure on moduli space if a Kahler form \omega is given on X. Such structures give a possible way to define K-theoretic Donaldson invariants. Though a symplectic structure could be defined on the top stratum of the moduli space, there are still some problems unsettled. For example, on lower strata, whether the structure is preserved under Taubes gluing construction and what could be done if \omega is a symplectic form rather than Kahler form. I will also talk about possible ways to solve these problems.