Ho N.-K. Yang-Mills connections on orientable and nonorientable surfaces / Ho N.-K., Liu C.-C.M. - Providence, R.I.: American Mathematical Society, 2009. - vii, 98 p. - (Memoirs of the American Mathematical Society; Vol.202, N 948). - Bibliogr.: p.97-98. - ISBN 978-0-8218-4491-5; ISSN 0065-9266  Место хранения:   013 | Институт математики СО РАН | Новосибирск | Библиотека

Оглавление / Contents

Acknowledgments ............................................... vii Chapter 1 Introduction ......................................... 1 Chapter 2 Topology of Gauge Group .............................. 5 Chapter 3 Holomorphic Principal Bundles over Riemann Surfaces ............................................. 9 3.1 Preliminaries on reductive Lie groups and Lie algebras ..... 9 3.2 Harder-Narasimhan filtrations of dual vector bundles ...... 12 3.3 Atiyah-Bott points ........................................ 12 3.4 Atiyah-Bott points for classical groups ................... 14 Chapter 4 Yang-Mills Connections and Representation Varieties ............................................ 19 4.1 Representation varieties for Yang-Mills connections ....... 19 4.2 Connected components of the representation variety for orientable surfaces ....................................... 20 4.3 Equivariant Poincare series ............................... 22 4.4 Involution on the Weyl Chamber ............................ 25 4.5 Connected components of the representation variety for nonorientable surfaces .................................... 27 4.6 Twisted representation varieties: U(n) .................... 29 4.7 Twisted representation varieties: SO(n) ................... 32 Chapter 5 Yang-Mills SO(2n + l)-Connections .................... 37 5.1 SO(2n + l)-connections on orientable surfaces ............. 37 5.2 Equivariant Poincare series ............................... 42 5.3 SO(2n + l)-connections on nonorientable surfaces .......... 44 Chapter 6 Yang-Mills SO(2n)-Connections ....................... 53 6.1 SO(2n)-connections on orientable surfaces ................. 53 6.2 Equivariant Poincare series ............................... 59 6.3 SO(4m + 2)-connections on nonorientable surfaces .......... 62 6.4 SO(4m)-connections on nonorientable surfaces .............. 68 Chapter 7 Yang-Mills Sp(n)-Connections ........................ 79 7.1 Sp(n)-connections on orientable surfaces .................. 79 7.2 Equivariant Poincare series ............................... 82 7.3 Sp(n)-connections on nonorientable surfaces ............... 84 Appendix A Remarks on Laumon-Rapoport Formula ................. 89 A.l Notation .................................................. 89 A.2 Inversion formulas ........................................ 91 A.3 Inversion of the Atiyah-Bott recursion relation ........... 94 Bibliography ................................................... 97