The caloron correspondence and higher string classes for loop groups

Details The caloron correspondence and higher string classes for loop groups The caloron correspondence and higher string classes for loop groups

2009-11-18

arxiv.org/abs/0911.3464v2

J. Geom. Phys., 60(9):1235-1250, 2010

Mathematics

Differential Geometry

21 pages. Author addresses added

Scientific paper

10.1016/j.geomphys.2010.04.010

We review the caloron correspondence between $G$-bundles on $M \times S^1$ and $\Omega G$-bundles on $M$, where $\Omega G$ is the space of smooth loops in the compact Lie group $G$. We use the caloron correspondence to define characteristic classes for $\Omega G$-bundles, called string classes, by transgression of characteristic classes of $G$-bundles. These generalise the string class of Killingback to higher dimensional cohomology.

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