The prequantum line bundle on the moduli space of flat $SU(N)$ connections on a Riemann surface and the homotopy of the large $N$ limit

Abstract

We show that the prequantum line bundle on the moduli space of flat $SU(2)$ connections on a closed Riemann surface of positive genus has degree 1. It then follows from work of Lawton and the second author that the classifying map for this line bundle induces a homotopy equivalence between the stable moduli space of flat $SU(N)$ connections, in the limit as $N$ tends to infinity, and $\mathbb{C}{P}^{\infty }$. Applications to the stable moduli space of flat unitary connections are also discussed.

7 pages. Version 3 contains various minor revisions

References in corpus (2)

• Fundamental Groups of Character Varieties: Surfaces and Tori
• Covering spaces of character varieties

Cited by in corpus (2)

• Covering spaces of character varieties
• Explicit Poincaré duality in the cohomology ring of the SU(2) character variety of a surface