Higher gauge theory. (English) Zbl 1132.55007

Baez, John C.; Schreiber, Urs

Davydov, Alexei (ed.) et al., Categories in algebra, geometry and mathematical physics. Conference and workshop in honor of Ross Street’s 60th birthday, Sydney and Canberra, Australia, July 11–16/July 18–21, 2005. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-3970-6/pbk). Contemporary Mathematics 431, 7-30 (2007).

In this survey paper the authors summarize the main ideas and results of their approach to higher gauge theories. The key tool is internalization, which leads to the concept of principal 2-bundles and 2-connections on these bundles. In this framework it is possible to define parallel transport along paths and surfaces in a natural parametrization-independent way.
For the entire collection see [Zbl 1116.18001].

Reviewer: József Szilasi (Debrecen)

MSC:

55R65	Generalizations of fiber spaces and bundles in algebraic topology
70S15	Yang-Mills and other gauge theories in mechanics of particles and systems
22A22	Topological groupoids (including differentiable and Lie groupoids)
53C05	Connections (general theory)
18A99	General theory of categories and functors

Keywords:

higher gauge theory; principal 2-bundles; 2-connections