Homology, Homotopy and Applications

Smooth functors vs. differential forms

Urs Schreiber and Konrad Waldorf

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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.

Article information

Source
Homology Homotopy Appl., Volume 13, Number 1 (2011), 143-203.

Dates
First available in Project Euclid: 29 July 2011

Permanent link to this document
https://projecteuclid.org/euclid.hha/1311953350

Mathematical Reviews number (MathSciNet)
MR2803871

Zentralblatt MATH identifier
1230.53025

Subjects
Primary: 53C05: Connections, general theory 18F15: Abstract manifolds and fiber bundles [See also 55Rxx, 57Pxx] 55R65: Generalizations of fiber spaces and bundles

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

Citation

Schreiber, Urs; Waldorf, Konrad. Smooth functors vs. differential forms. Homology Homotopy Appl. 13 (2011), no. 1, 143--203. https://projecteuclid.org/euclid.hha/1311953350


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