A Cubical Set Approach to 2-Bundles with Connection and Wilson Surfaces

Abstract

In the context of non-abelian gerbes we define a cubical version of categorical group 2-bundles with connection over a smooth manifold. We define their two-dimensional parallel transport, study its properties, and define non-abelian Wilson surface functionals.

Improvement on the exposition. Approximately 60 pages, 2 figures

References in corpus (11)

• Higher-Dimensional Algebra V: 2-Groups
• Higher Gauge Theory: 2-Connections on 2-Bundles
• Higher Yang-Mills Theory
• Parallel Transport and Functors
• Higher gauge theory I: 2-Bundles
• Categorical representations of categorical groups
• The Fundamental Crossed Module of the Complement of a Knotted Surface
• The inner automorphism 3-group of a strict 2-group
• Smooth Functors vs. Differential Forms
• Thin Elements and Commutative Shells in Cubical omega-categories
• Lie 2-Algebras

Cited by in corpus (8)

• An Invitation to Higher Gauge Theory
• Twisted differential String and Fivebrane structures
• Teleparallel Gravity as a Higher Gauge Theory
• A new formulation of higher parallel transport in higher gauge theory
• Transformation Double Categories Associated to 2-Group Actions
• On higher holonomy invariants in higher gauge theory II
• Quantum surface holonomies for loop quantum gravity and their application to black hole horizons
• Parallel 2-transport and 2-group torsors