String structures and the path fibration of a group |
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Authors: | A L Carey M K Murray |
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Institution: | (1) Department of Pure Mathematics, University of Adelaide, GPO Box 498, 5001 Adelaide, SA, Australia;(2) Mathematics Research Section, School of Mathematical Sciences, Institute of Advanced Studies, The Australian National University, GPO Box 4, 2601 Canberra, ACT, Australia |
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Abstract: | We use the realisation of the universal bundle for the loop group as the path fibration of the group to investigate the string class, that is the obstruction to a loop group bundle lifting to a Kac-Moody group bundle. In the case that the loop group bundle is constructed by taking loops into a principal bundle we show that the classifying map is the holonomy around loops and give an explicit formula for the string class relating it to the Pontrjangin class of the principal bunble. |
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