The caloron correspondence and higher string classes for loop groups

Abstract

We review the caloron correspondence between G-bundles on M × S1 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. © 2010 Elsevier B.V.