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A LOOP SPACE FORMULATION FOR GEOMETRIC LIFTING PROBLEMS

Published online by Cambridge University Press:  09 June 2011

KONRAD WALDORF*
Affiliation:
Department of Mathematics, University of California, 970 Evans Hall #3840, Berkeley, CA 94720, USA
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Abstract

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We review and then combine two aspects of the theory of bundle gerbes. The first concerns lifting bundle gerbes and connections on those, developed by Murray and by Gomi. Lifting gerbes represent obstructions against extending the structure group of a principal bundle. The second is the transgression of gerbes to loop spaces, initiated by Brylinski and McLaughlin and with recent contributions of the author. Combining these two aspects, we obtain a new formulation of lifting problems in terms of geometry on the loop space. Most prominently, our formulation explains the relation between (complex) spin structures on a Riemannian manifold and orientations of its loop space.

Type
Research Article
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

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