Polysymplectic Reduction and the Moduli Space of Flat Connections
发布人: 曹思圆   发布时间: 2019-01-02   浏览次数: 12

报告人:Dr. Casey Blacker(华东师范大学)

时间地点:2018年1月3日,周四, 13:00-14:00,数学楼102(闵行校区)


In a landmark paper, Atiyah and Bott showed that the moduli space of flat connections on a principal bundle over an orientable closed surface is the symplectic reduction of the space of all connections by the action of the gauge group. By appealing to polysymplectic geometry, a generalization of symplectic geometry in which the symplectic form takes values in a given vector space, we may extend this result to the case of higher-dimensional base manifolds. In this setting, the space of connections possesses a natural polysymplectic structure, and the polysymplectic reduction of this space by the action of the gauge group yields the moduli space of flat connections equipped with a 2-form taking values in the cohomology of the base manifold. In this talk, based on the recent preprint arXiv:1810.04924, I will first review the polysymplectic formalism and then outline its role in obtaining the moduli space of flat connections.