1983/03/17 by Michael Francis Atiyah, Raoul Bott · 4 citations
paper · doi:10.1098/rsta.1983.0017
crossref issued 1983/03/17 · crossref published 1983/03/17 · crossref published-print 1983/03/17 · crossref created 2006/12/18 · crossref deposited 2026/02/26 · crossref indexed 2026/08/01
Abstract The Yang-Mills functional over a Riemann surface is studied from the point of view of Morse theory. The main result is that this is a ‘perfect' functional provided due account is taken of its gauge symmetry. This enables topological conclusions to be drawn about the critical sets and leads eventually to information about the moduli space of algebraic bundles over the Riemann surface. This in turn depends on the interplay between the holomorphic and unitary structures, which is analysed in detail.