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2011 Smooth functors vs. differential forms
Urs Schreiber, Konrad Waldorf
Homology Homotopy Appl. 13(1): 143-203 (2011).

Abstract

We establish a relation between smooth 2-functors defined on the path 2-groupoid of a smooth manifold and differential forms on this manifold. This relation can be understood as a part of a dictionary between fundamental notions from category theory and differential geometry. We show that smooth 2-functors appear in several fields, namely as connections on (non-abelian) gerbes, as derivatives of smooth functors and as critical points in BF theory. We demonstrate further that our dictionary provides a powerful tool to discuss the transgression of geometric objects to loop spaces.

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Urs Schreiber. Konrad Waldorf. "Smooth functors vs. differential forms." Homology Homotopy Appl. 13 (1) 143 - 203, 2011.

Information

Published: 2011
First available in Project Euclid: 29 July 2011

zbMATH: 1230.53025
MathSciNet: MR2803871

Subjects:
Primary: 18F15 , 53C05 , 55R65

Keywords: 2-group , Connection , gerbe , parallel transport , path 2-groupoid

Rights: Copyright © 2011 International Press of Boston

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Vol.13 • No. 1 • 2011
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