The caloron correspondence and higher string classes for loop groups

We review the caloron correspondence between $G$-bundles on $M \times S^1$ and $ΩG$-bundles on $M$, where $ΩG$ is the space of smooth loops in the compact Lie group $G$. We use the caloron correspondence to define characteristic classes for $ΩG$-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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