Homotopy decompositions of P U (n) -gauge groups over Riemann surfaces

Abstract

In this paper, we show that the gauge group of a principal PU(n)-bundle over a compact Riemann surface decomposes up to homotopy as the product of factors, one of which is a corresponding gauge group for S2 and the others are immediately recognizable spaces. Further, when n is a prime p, the gauge group for S2 decomposes as a product of immediately recognizable factors. These gauge groups have strong connections to moduli spaces of stable vector bundles.