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
  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. 
Lisa C. Jeffrey, Daniel A. Ramras, and Jonathan Weitsman
math.AT math-ph math.DG math.MP math.SG