In this easy introduction to higher gauge theory, we describe parallel transport for particles
and strings in terms of 2-connections on 2-bundles. Just as ordinary gauge theory involves a …

To answer some issues raised about the concept of fractional differentiation and integration
based on the exponential and Mittag-Leffler laws, we present, in this paper, fundamental …

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 …

We construct a prequantum 2-Hilbert space for any line bundle gerbe whose Dixmier–
Douady class is torsion. Analogously to usual prequantization, this 2-Hilbert space has the …

In this paper, we introduce the notions of hom-Lie 2-algebras, which is the categorification of
hom-Lie algebras, HL∞-algebras, which is the hom-analogue of L∞-algebras, and crossed …

We present an extended version of Riemannian geometry suitable for the description of
current formulations of double field theory (DFT). This framework is based on graded …

The (pre) multisymplectic geometry of the De Donder–Weyl formalism for field theories is
further developed for a variety of field theories including a scalar field theory from the …

A manifold is multisymplectic, or more specifically n-plectic, if it is equipped with a closed
nondegenerate differential form of degree n+ 1. In previous work with Baez and Hoffnung …

We investigate a class of Leibniz algebroids which are invariant under diffeomorphisms and
symmetries involving collections of closed forms. Under appropriate assumptions we arrive …

We implement in the formal language of homotopy type theory a new set of axioms called
cohesion. Then we indicate how the resulting cohesive homotopy type theory naturally …