Related papers: Multiplicative Bundle Gerbes with Connection
We use bundle gerbes and their connections and curvings to obtain an explicit formula for a de Rham representative of the string class of a loop group bundle. This is related to earlier work on calorons.
Let $M$ be a smooth manifold and let $\chi\in \Omega^3(M)$ be closed differential form with integral periods. We show the Lie 2-algebra of sections of the $\chi$-twisted Courant algebroid on $M$ is quasi-isomorphic to the Lie 2-algebra of…
The coupling of the tangent bundle $TM$ with the Lie algebra bundle $L$ (K.Mackenzie,2005, Definition 7.2.2) plays the crucial role in the classification of the transitive Lie algebroids for Lie algebra bundle $L$ with fixed finite…
We show that the category of abelian gerbes over a smooth manifold is equivalent to a certain category of principal bundles over the free loop space. These principal bundles are equipped with fusion products and are equivariant with respect…
Characteristic properties of corings with a grouplike element are analysed. Associated differential graded rings are studied. A correspondence between categories of comodules and flat connections is established. A generalisation of the…
We give a review of truncated L$_\infty$ algebras, as used in the study of higher gauge theory. These structures are believed to hold the correct properties to adequately describe gauge theory of extended objects. We discuss how to…
These notes survey the theory of (twisted) conformal blocks from an algebro-geometric perspective and have two main goals. The first one is to summarize the construction of conformal blocks from vertex operator algebras, and to describe…
We prove that smooth, separated Deligne--Mumford stacks in mixed characteristic with quasi-projective coarse moduli space are global quotient stacks and satisfy the resolution property. This builds on work of Kresch and Vistoli and of…
We define and investigate a geometric object, called an associative geometry, corresponding to an associative algebra (and, more generally, to an associative pair). Associative geometries combine aspects of Lie groups and of generalized…
We define and investigate a geometric object, called an associative geometry, corresponding to an associative algebra (and, more generally, to an associative pair). Associative geometries combine aspects of Lie groups and of generalized…
Let $\mathcal{G}$ be a bundle gerbe with connection on a smooth manifold $M$, and let $\rho: G \rightarrow \operatorname{Diff}(M)$ be a smooth action of a Fr\'echet--Lie group $G$ on $M$ that preserves the isomorphism class of…
We provide a pedagogical introduction to the theory of principal 2-bundles with adjusted connections and show how they enter the description of geometric and non-geometric T-dualities as proposed in arXiv:2204.01783. This description…
Conformal blocks form a system of vector bundles over the moduli space of complex curves with marked points. We discuss various aspects of these bundles. In particular, we present conjectures about the dimensions of sub-bundles. They imply…
This paper reviews recent work on a new geometric object called a bundle gerbe and discusses some new examples arising in quantum field theory. One application is to an Atiyah-Patodi-Singer index theory construction of the bundle of…
We introduce multiplicative Ehresmann connections on surjective submersions of Lie groupoids, extending both the classical notion of Ehresmann connections on fibre bundles and the more recent notion of multiplicative connections on Lie…
Abelian gerbes and twisted bundles describe the topology of the NS-NS 3-form gauge field strength H. We review how they have been usefully applied to study and resolve global anomalies in open string theory. Abelian 2-gerbes and twisted…
We describe Legendrian surgery diagrams for some horizontal contact structures on non-positive plumbing trees of oriented circle bundles over spheres with negative Euler numbers. As an application we determine Milnor fillable contact…
This masters thesis reviews bundle gerbe theory and the well-known basic bundle gerbe over SU(n). We introduce the cup product bundle gerbe, and show it is stably isomorphic to the pullback of the basic bundle gerbe by the Weyl map. This…
We define metric bundles/metric graph bundles which provide a purely topological/coarse-geometric generalization of the notion of trees of metric spaces a la Bestvina-Feighn in the special case that the inclusions of the edge spaces into…
In this paper we generalize the theory of multiplicative $G$-Higgs bundles over a curve to pairs $(G,\theta)$, where $G$ is a reductive algebraic group and $\theta$ is an involution of $G$. This generalization involves the notion of a…