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arXiv · 0911.3464

The caloron correspondence and higher string classes for loop groups

Michael K. Murray·Raymond F. Vozzo
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Abstract

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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Michael K. Murray, Raymond F. Vozzo. 2009-11-18. The caloron correspondence and higher string classes for loop groups. https://doi.org/10.1016/j.geomphys.2010.04.010

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