Related papers: Central Extensions of Smooth 2-Groups and a Finite…

Let $\Gamma$ be a finite dimensional Lie group and consider the smooth double loop group, i.e. the Fr\'echet Lie group of smooth maps from the 2-torus to $\Gamma$. For a finite dimensional Hilbert space V, let H denote the Hilbert space of…

We construct a model for the string group as an infinite-dimensional Lie group. In a second step we extend this model by a contractible Lie group to a Lie 2-group model. To this end we need to establish some facts on the homotopy theory of…

We deal with the symmetries of a (2-term) graded vector space or bundle. Our first theorem shows that they define a (strict) Lie 2-groupoid in a natural way. Our second theorem explores the construction of nerves for Lie 2-categories,…

We provide a general, homotopy-theoretic definition of string group models within an $\infty$-category of smooth spaces, and we present new smooth models for the string group. Here, a smooth space is a presheaf of $\infty$-groupoids on the…

We study bundle gerbes on manifolds $M$ that carry an action of a connected Lie group $G$. We show that these data give rise to a smooth 2-group extension of $G$ by the smooth 2-group of hermitean line bundles on $M$. This 2-group extension…

We study the smooth $2$-group structure arising in the presence of quantum field theory with one-form symmetry. We acquire $2$-group structures obtained by a central extension of the zero-form symmetry by the one-form symmetry. We determine…

Categorifying the concept of topological group, one obtains the notion of a 'topological 2-group'. This in turn allows a theory of 'principal 2-bundles' generalizing the usual theory of principal bundles. It is well-known that under mild…

We give a complete and explicit description of the kinematical data of higher gauge theory on principal 2-bundles with the string 2-group model of Schommer-Pries as structure 2-group. We start with a self-contained review of the weak…

We study monoidal 2-categories and bicategories in terms of categorical extensions and the cohomological data they determine in appropriate cohomology theories with coefficients in Picard groupoids. In particular, we analyze the hierarchy…

For a weak 2-group, we construct a bicategory of flat 2-group bundles over differentiable stacks as a localization of a functor bicategory. This description is amenable to explicit geometric constructions. For example, we show that flat…

We associate to a 2-vector bundle over an essentially finite groupoid a 2-vector space of parallel sections, or, in representation theoretic terms, of higher invariants, which can be described as homotopy fixed points. Our main result is…

We present an explicit construction for the central extension of the group $\Map(X, G)$ where $X$ is a compact manifold and $G$ is a Lie group. If $X$ is a complex curve we obtain a simple construction of the extension by the Picard variety…

We construct a central Lie group extension for the Lie group of compactly supported sections of a Lie group bundle over a sigma-compact base manifold. This generalises a result of the paper "Central extensions of groups of sections" by Neeb…

We develop a ready-to-use comprehensive theory for (super) 2-vector bundles over smooth manifolds. It is based on the bicategory of (super) algebras, bimodules, and intertwiners as a model for 2-vector spaces. We discuss symmetric monoidal…

I categorify the definition of fibre bundle, replacing smooth manifolds with differentiable categories, Lie groups with coherent Lie 2-groups, and bundles with a suitable notion of 2-bundle. To link this with previous work, I show that…

We give a very simple construction of the string 2-group as a strict Fr\'echet Lie 2-group. The corresponding crossed module is defined using the conjugation action of the loop group on its central extension, which drastically simplifies…

We recall Schur's work on universal central extensions and develop the analogous theory for categorical extensions of groups. We prove that the String 2-groups are universal in this sense and study in detail their restrictions to the finite…

We begin with a brief sketch of what is known and conjectured concerning braided monoidal 2-categories and their applications to 4d topological quantum field theories and 2-tangles (surfaces embedded in 4-dimensional space). Then we give…

Presentations of smooth symmetry groups of differentiable stacks are studied within the framework of the weak 2-category of Lie groupoids, smooth principal bibundles, and smooth biequivariant maps. It is shown that principality of bibundles…

In this paper, we address the construction of homotopy bicategories of $(\infty,2)$-categories, which we take as being modeled by 2-fold Segal spaces. Our main result is the concrete construction of a functor $h_2$ from the category of…