We study topological defect lines in two-dimensional rational conformal field theory.
Continuous variation of the location of such a defect does not change the value of a …

We formulate differential cohomology and Chern-Weil theory--the theory of connections on
fiber bundles and of gauge fields--abstractly in the context of a certain class of higher …

The theory of principal bundles makes sense in any ∞∞-topos, such as the ∞∞-topos of
topological, of smooth, or of otherwise geometric ∞∞-groupoids/∞∞-stacks, and more …

To set the scene, we begin here by reviewing basics of homotopy theory via model category
theory [Quillen (1967)](review in [Hovey (1999)][Hirschhorn (2003)][Lurie (2009a), A. 2]) and …

We introduce an axiomatic framework for the parallel transport of connections on gerbes. It
incorporates parallel transport along curves and along surfaces, and is formulated in terms …

Parallel transport of a connection in a smooth fibre bundle yields a functor from the path
groupoid of the base manifold into a category that describes the fibres of the bundle. We …

In this book we prove (Thm. 4. 3.24) unified classification results for stable equivariant Γ-
principal bundles when the underlying homotopy type SΓ of the topological structure group Γ …

This is an invited survey article on higher gauge theory for the Encyclopedia of Mathematical
Physics, 2nd edition. In particular, we provide a lightning introduction to higher structures …

We recall and partially improve four versions of smooth, nonabelian gerbes: Čech cocycles,
classifying maps, bundle gerbes, and principal 2-bundles. We prove that all four versions …

In this paper, we discuss decomposition in the context of three-dimensional Chern–Simons
theories. Specifically, we argue that a Chern–Simons theory with a gauged noneffectively …