String connections and Chern-Simons theory

Waldorf, Konrad

doi:10.1090/S0002-9947-2013-05816-3

Author: Konrad Waldorf
Journal: Trans. Amer. Math. Soc. 365 (2013), 4393-4432
MSC (2010): Primary 53C08; Secondary 57R56, 57R15
DOI: https://doi.org/10.1090/S0002-9947-2013-05816-3
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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