Yang-Mills Connections on Nonorientable Surfaces

Details Yang-Mills Connections on Nonorientable Surfaces Yang-Mills Connections on Nonorientable Surfaces

2006-05-22

arxiv.org/abs/math/0605587v3

Comm. Anal. Geom. 16 (2008), no.3, 617-679

Mathematics

Symplectic Geometry

45 pages, 1 figure

Scientific paper

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. We generalize their study to all closed, compact, connected, possibly nonorientable surfaces. We introduce the notion of "super central extension" of the fundamental group of a surface. It is the central extension when the surface is orientable. We establish a precise correspondence between Yang-Mills connections and representations of super central extension. Knowing this exact correspondence, we work mainly at the level of representation varieties which are finite dimensional instead of the level of strata which are infinite dimensional.

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