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 …

What are called secondary characteristic classes in Chern–Weil theory are a refinement of
ordinary characteristic classes of principal bundles from cohomology to differential …

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 …

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 discuss two aspects of the presentation of the theory of principal ∞∞-bundles in an ∞∞-
topos, introduced in Nikolaus et al.(Principal ∞∞-bundles: general theory, 2012), in terms of …

Abstract We establish a Penrose–Ward transform yielding a bijection between holomorphic
principal 2-bundles over a twistor space and non-Abelian self-dual tensor fields on six …

In the presence of a nonzero B-field, the symmetries of the E8× E 8 heterotic string form a 2-
group, or a categorified group, as do the symmetries of the CHL string. We express the …

We extend the Chern character on K-theory, in its generalization to the Chern-Dold
character on generalized cohomology theories, further to (twisted, differential) non-abelian …

The classical Chern correspondence states that a choice of Hermitian metric on a
holomorphic vector bundle determines uniquely a unitary'Chern connection'. This basic …