# Principal ∞-Bundles and Smooth String Group Models

@inproceedings{Bunk2020PrincipalA, title={Principal ∞-Bundles and Smooth String Group Models}, author={Severin Bunk}, year={2020} }

We provide a general, homotopy-theoretic definition of string group models within an ∞-category of smooth spaces, and we present new smooth models for the string group. Here, a smooth space is a presheaf of ∞-groupoids on the category of cartesian spaces. The key to our definition and construction of smooth string group models is a version of the singular complex functor, which assigns to a smooth space an underlying ordinary space. We provide new characterisations of principal ∞-bundles and…

## 5 Citations

### TheR-local homotopy theory of smooth spaces

- Mathematics
- 2022

Simplicial presheaves on cartesian spaces provide a general notion of smooth spaces. There is a corresponding smooth version of the singular complex functor, which maps smooth spaces to simplicial…

### The $$\mathbb {R}$$-local homotopy theory of smooth spaces

- MathematicsJournal of Homotopy and Related Structures
- 2022

Simplicial presheaves on cartesian spaces provide a general notion of smooth spaces. There is a corresponding smooth version of the singular complex functor, which maps smooth spaces to simplicial…

### Gerbes in Geometry, Field Theory, and Quantisation

- MathematicsComplex Manifolds
- 2021

Abstract This is a mostly self-contained survey article about bundle gerbes and some of their recent applications in geometry, field theory, and quantisation. We cover the definition of bundle gerbes…

### The Drinfel'd centres of String 2-groups

- Mathematics
- 2022

Let G be a compact connected Lie group and k ∈ H 4 ( B G, Z ) a cohomology class. The String 2-group G k is the central extension of G by the 2-group [ ∗ /U (1)] classiﬁed by k . It has a close…

### A representation of the string 2-group

- Mathematics
- 2022

We construct a representation of the string 2-group on a 2-vector space, namely on the hyperfinite type III1 von Neumann algebra. We prove that associating this representation to the frame bundle of…

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