Loop groups, string classes and equivariant cohomology

Vozzo, R.F. (2011) Loop groups, string classes and equivariant cohomology. Journal of the Australian Mathematical Society, 90(1), pp. 109-127. (doi: 10.1017/S1446788711001066)

Abstract

We give a classifying theory for LG-bundles, where LG is the loop group of a compact Lie group G, and present a calculation for the string class of the universal LG-bundle. We show that this class is in fact an equivariant cohomology class and give an equivariant differential form representing it. We then use the caloron correspondence to define (higher) characteristic classes for LG-bundles and to prove a result for characteristic classes for based loop groups for the free loop group. These classes have a natural interpretation in equivariant cohomology and we give equivariant differential form representatives for the universal case in all odd dimensions.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Vozzo, Dr Raymond
• Authors: Vozzo, R.F.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Journal of the Australian Mathematical Society
• Journal Abbr.: J. Aust. Math. Soc.
• ISSN: 1446-7887
• Published Online: 22 March 2011