Yang-Mills Connections on Orientable and Nonorientable Surfaces
Author： Nan-Kuo Ho;Chiu-Chu Melissa Liu
Publisher： American Mathematical Society
Publication year： 2013
E-ISBN: 9781470405625
P-ISBN(Paperback): 9780821844915
P-ISBN(Hardback): 9780821844915
Subject： O186 Differential Geometry and Integral Geometry
Keyword： Geometry and Topology
Language： ENG
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Yang-Mills Connections on Orientable and Nonorientable Surfaces
Description
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 $Sp(n)$.