The second universal motivic Chern class and cluster structure of moduli spaces of G-local systems

Abstract: The second motivic Chern class is the generator of the degree 4, weight 2 motivic cohomology of BG, where G is a split simple algebraic group over Q. I will construct a collection of explicit cocycles for the second motivic Chern class. It has a number of applications, such as local combinatorial formulas for the usual second Chern class of a G-bundle over a manifold, or explicit constructions of the determinant bundle on Bun(G), the extension of G by K_2 etc. The construction is closely related to the cluster structure of the moduli space of decorated G-local systems on a surface S with boundary.

algebraic geometrysymplectic geometry

Audience: researchers in the topic

M-seminar