Topology of the space of commuting elements in SU(2)

Description

Let G be a Lie group. The moduli space of flat principal G-bundles over a manifold X is an important geometric object in mathematical physics due to its intimate relations with gauge theory and conformal field theory, which in turn shed light on its geometry and topology. When X is a torus, the moduli space is the space of commuting elements in G. The topology of the space of commuting elements has garnered some interest in recent years. In particular, the cohomology and K-theory of the space of commuting elements in SU(2) has been studied in various contexts. In this talk, we will present the ring structure of the integral cohomology and K-theory of the space of n commuting elements in SU(2) for any natural number n. We will also discuss the contrasting behaviour of the cohomology group with different coefficients in the context of representation stability. Time permitting, results of the case where the Lie group is SO(3) will be mentioned.

Period	26 Aug 2026
Held at	The Chinese University of Hong Kong, Shenzhen, China
Degree of Recognition	Local