Memoirs of the American Mathematical Society 2009; 98 pp; softcover Volume: 202 ISBN10: 0821844911 ISBN13: 9780821844915 List Price: US$69 Individual Members: US$41.40 Institutional Members: US$55.20 Order Code: MEMO/202/948
 In "The YangMills equations over Riemann surfaces", Atiyah and Bott studied YangMills functional over a Riemann surface from the point of view of Morse theory. In "YangMills Connections on Nonorientable Surfaces", the authors study YangMills functional on the space of connections on a principal \(G_{\mathbb{R}}\)bundle over a closed, connected, nonorientable surface, where \(G_{\mathbb{R}}\) is any compact connected Lie group. In this monograph, the authors generalize the discussion in "The YangMills equations over Riemann surfaces" and "YangMills Connections on Nonorientable Surfaces". They obtain explicit descriptions of equivariant Morse stratification of YangMills functional on orientable and nonorientable surfaces for nonunitary classical groups \(SO(n)\) and \(Sp(n)\). Table of Contents  Introduction
 Topology of Gauge group
 Holomorphic principal bundles over Riemann surfaces
 YangMills connections and representation varieties
 YangMills \(SO(2n+1)\)connections
 YangMills \(SO(2n)\)connections
 YangMills \(Sp(n)\)connections
 Appendix A. Remarks on LaumonRapoport formula
 Bibliography
