# Transgressive loop group extensions

@article{Waldorf2015TransgressiveLG, title={Transgressive loop group extensions}, author={Konrad Waldorf}, journal={Mathematische Zeitschrift}, year={2015}, volume={286}, pages={325-360} }

A central extension of the loop group of a Lie group is called transgressive, if it corresponds under transgression to a degree four class in the cohomology of the classifying space of the Lie group. Transgressive loop group extensions are those that can be explored by finite-dimensional, higher-categorical geometry over the Lie group. We show how transgressive central extensions can be characterized in a loop-group theoretical way, in terms of loop fusion and thin homotopy equivariance.

#### 9 Citations

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We classify central extensions of a reductive group $G$ by $\mathcal{K}_3$ and $B\mathcal{K}_3$, the sheaf of third Quillen $K$-theory groups and its classifying stack. These turn out to be… Expand

Loop groups and noncommutative geometry

- Mathematics, Physics
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We describe the representation theory of loop groups in terms of K-theory and noncommutative geometry. This is done by constructing suitable spectral triples associated with the level l projective… Expand

Connes fusion of spinors on loop space

- Mathematics, Physics
- 2020

The loop space of a string manifold supports an infinite-dimensional Fock space bundle, which is an analog of the spinor bundle on a spin manifold. This spinor bundle on loop space appears in the… Expand

The Spinor Bundle on Loop Space and its Fusion product

- Physics
- 2020

Given a manifold with a string structure, we construct a spinor bundle on its loop space. Our construction is in analogy with the usual construction of a spinor bundle on a spin manifold, but… Expand

String geometry vs. spin geometry on loop spaces

- Mathematics, Physics
- 2015

Abstract We introduce various versions of spin structures on free loop spaces of smooth manifolds, based on a classical notion due to Killingback, and additionally coupled to two relations between… Expand

The classification of chiral WZW models by H4 +(BG, ℤ)

- Mathematics
- 2017

We axiomatize the defining properties of chiral WZW models. We show that such models are in almost bijective correspondence with pairs (G, k), where G is a connected Lie group and k ∈ H4 + (BG, ℤ) is… Expand

Fusion of implementers for spinors on the circle.

- Mathematics
- 2019

We consider the space of odd spinors on the circle, and a decomposition into spinors supported on either the top or on the bottom half of the circle. If an operator preserves this decomposition, and… Expand

The classification of chiral WZW models by $H^4_+(BG,\mathbb Z)$

- Mathematics, Physics
- 2016

We axiomatize the defining properties of chiral WZW models. We show that such models are in almost bijective correspondence with pairs $(G,k)$, where $G$ is a connected Lie group and $k \in… Expand

What Chern–Simons theory assigns to a point

- Mathematics, Medicine
- Proceedings of the National Academy of Sciences
- 2017

It is proved that, modulo certain conjectures, the category of representations of the based loop group is a bicommutant category, and it puts Turaev–Viro theories and Reshetikhin–Turaev theories on an equal footing by providing a unified language, bicomutant categories, that applies to both. Expand

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