Yang-Mills Connections on Orientable and Nonorientable Surfaces

Buch | Softcover

98 Seiten

2010
American Mathematical Society (Verlag)
978-0-8218-4491-5 (ISBN)

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Studies the Yang-Mills 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. They obtain explicit descriptions of equivariant Morse stratification of Yang-Mills functional on orientable and nonorientable surfaces for non-unitary classical groups $SO(n)$ and $Sp(n)$.

In ""The Yang-Mills equations over Riemann surfaces"", Atiyah and Bott studied Yang-Mills functional over a Riemann surface from the point of view of Morse theory. In ""Yang-Mills Connections on Nonorientable Surfaces"", the authors study Yang-Mills 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 Yang-Mills equations over Riemann surfaces"" and ""Yang-Mills Connections on Nonorientable Surfaces"". They obtain explicit descriptions of equivariant Morse stratification of Yang-Mills functional on orientable and nonorientable surfaces for non-unitary classical groups $SO(n)$ and $Sp(n)$.

Introduction; Topology of Gauge group; Holomorphic principal bundles over Riemann surfaces; Yang-Mills connections and representation varieties; Yang-Mills $SO(2n+1)$-connections; Yang-Mills $SO(2n)$-connections; Yang-Mills $Sp(n)$-connections; Appendix A. Remarks on Laumon-Rapoport formula; Bibliography.

Erscheint lt. Verlag	26.1.2010
Reihe/Serie	Memoirs of the American Mathematical Society
Verlagsort	Providence
Sprache	englisch
Gewicht	180 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
ISBN-10	0-8218-4491-1 / 0821844911
ISBN-13	978-0-8218-4491-5 / 9780821844915
Zustand	Neuware