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

摘要

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 thenfollows from work of Lawton and the second author that the classifying map forthis line bundle induces a homotopy equivalence between the stable moduli spaceof 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 unitaryconnections are also discussed.