Related papers: An Introduction to Bundle Gerbes

This article is devoted to the investigation of structure of wrap groups of fiber bundles over ultra-normed infinite fields and more generally over Cayley-Dickson algebras. Iterated wrap groups are studied as well. Their smashed products…

We make the category BGrb_M of bundle gerbes on a manifold M into a 2-category by providing 2-cells in the form of transformations of bundle gerbe morphisms. This description of BGrb_M as a 2-category is used to define the notion of a…

We prove that the category of abelian gerbes with connection over a smooth manifold is equivalent to a certain category of principal bundles over the free loop space. These bundles are equipped with a connection and with a "fusion" product…

In this Note, we propose a line bundle approach to odd-dimensional analogues of generalized complex structures. This new approach has three main advantages: (1) it encompasses all existing ones; (2) it elucidates the geometric meaning of…

A continuous cohomology theory for topological quandles is introduced, and compared to the algebraic theories. Extensions of topological quandles are studied with respect to continuous 2-cocycles, and used to show the differences in second…

This is the expanded text of a series of CIME lectures. We present an algebro-geometric approach to integrable systems, starting with those which can be described in terms of spectral curves. The prototype is Hitchin's system on the…

We elaborate on the construction of a prequantum 2-Hilbert space from a bundle gerbe over a 2-plectic manifold, providing the first steps in a program of higher geometric quantisation of closed strings in flux compactifications and of…

We develop a gauge theory or theory of bundles and connections on them at the level of braids and tangles. Extending recent algebraic work, we provide now a fully diagrammatic treatment of principal bundles, a theory of global gauge…

Given a smooth projective complex curve $X$ with an involution $\sigma$, we study the Hitchin systems for the locus of anti-invariant (resp. invariant) stable vector bundles over $X$ under $\sigma$. Using these integrable systems and the…

We give a geometric interpretation of sheaf cohomology for higher degrees n in terms of torsors on the member of degree d=n-1 in hypercoverings of type r=n-2, endowed with an additional data, the so-called rigidification. This generalizes…

Projective spaces for finite-dimensional vector spaces over general fields are considered. The geometry of these spaces and the theory of line bundles over these spaces is presented. Particularly, the space of global regular sections of…

The topological classification of gerbes, as principal bundles with the structure group the projective unitary group of a complex Hilbert space, over a topological space $H$ is given by the third cohomology $\text{H}^3(H, \Bbb Z)$. When $H$…

We introduce a notion of ternary distributive algebraic structure, give examples, and relate it to the notion of a quandle. Classification is given for low order structures of this type. Constructions of such structures from ternary…

The aim of this talk is to explain how symmetry breaking in a quantum field theory problem leads to a study of projective bundles, Dixmier-Douady classes, and associated gerbes. A gerbe manifests itself in different equivalent ways. Besides…

In this paper, we describe the spectral correspondence for cyclic Higgs bundles from the viewpoint of quiver bundles. Under this framework, we establish a one-to-one correspondence between cyclic Higgs bundles on a curve and sheaves on a…

We study various aspects on nontrivial logarithmic co-Higgs structure associated to unstable bundles on algebraic curves. We check several criteria for (non-)existence of nontrivial logarithmic co-Higgs structures and describe their…

Local connection forms provide a very useful tool for handling connections on principal bundles, because they ignore any complexities of the total space and, essentially, involve only two fundamental features of the structure group, namely…

We study Higgs bundles over an elliptic curve with complex reductive structure group, describing the (normalization of) its moduli spaces and the associated Hitchin fibration. The case of trivial degree is covered by the work of Thaddeus in…

We study the basic properties of Higgs sheaves over compact K\"ahler manifolds and we establish some results concerning the notion of semistability; in particular, we show that any extension of semistable Higgs sheaves with equal slopes is…

In the first part the sh Lie structure of brackets in field theory, described in the jet bundle context along the lines suggested by Gel'fand, Dickey and Dorfman, is analyzed. In the second part, we discuss how this description allows us to…