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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



String connections and Chern-Simons theory

Author: Konrad Waldorf
Journal: Trans. Amer. Math. Soc. 365 (2013), 4393-4432
MSC (2010): Primary 53C08; Secondary 57R56, 57R15
Published electronically: March 5, 2013
MathSciNet review: 3055700
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Abstract: We present a finite-dimensional and smooth formulation of string structures on spin bundles. It uses trivializations of the Chern-Simons 2-gerbe associated to this bundle. Our formulation is particularly suitable to deal with string connections: it enables us to prove that every string structure admits a string connection and that the possible choices form an affine space. Further we discover a new relation between string connections, 3-forms on the base manifold, and degree three differential cohomology. We also discuss in detail the relation between our formulation of string connections and the original version of Stolz and Teichner.

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Konrad Waldorf
Affiliation: Department of Mathematics, 970 Evans Hall #3840, University of California, Berkeley, Berkeley, California 94720
Address at time of publication: Fakultät für Mathematik, Universität Regensburg, Universitätsstrasse 31, 93053 Regensburg, Germany

Received by editor(s): June 30, 2011
Received by editor(s) in revised form: January 29, 2012
Published electronically: March 5, 2013
Additional Notes: The author gratefully acknowledges support by a Feodor-Lynen scholarship, granted by the Alexander von Humboldt Foundation. The author thanks Martin Olbermann, Arturo Prat-Waldron, Urs Schreiber and Peter Teichner for exciting discussions, and two referees for their helpful comments and suggestions.
Article copyright: © Copyright 2013 by the author

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