# Principal ∞-bundles - General theory

@inproceedings{Nikolaus2012Principal, title={Principal ∞-bundles - General theory}, author={Thomas Nickelsen Nikolaus and Urs Schreiber and Danny Stevenson}, year={2012} }

The theory of principal bundles makes sense in any ∞-topos, such as the ∞-topos of topological, of smooth, or of otherwise geometric ∞-groupoids/∞-stacks, and more generally in slices of these. It provides a natural geometric model for structured higher nonabelian cohomology and controls general fiber bundles in terms of associated bundles. For suitable choices of structure ∞-group G these G-principal ∞-bundles reproduce the theories of ordinary principal bundles, of bundle gerbes/principal 2…

## 80 Citations

### Principal ∞-Bundles and Smooth String Group Models

- Mathematics
- 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…

### Smooth 2-Group Extensions and Symmetries of Bundle Gerbes

- MathematicsCommunications in Mathematical Physics
- 2021

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…

### Fluxes, bundle gerbes and 2-Hilbert spaces

- Mathematics
- 2016

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 programme of higher geometric quantisation of closed…

### Categorical structures on bundle gerbes and higher geometric prequantisation

- Mathematics
- 2017

We present a construction of a 2-Hilbert space of sections of a bundle gerbe, a suitable candidate for a prequantum 2-Hilbert space in higher geometric quantisation. We introduce a direct sum on the…

### A CHARACTERISTIC EXACT SEQUENCE FOR PRINCIPAL BUNDLES

- Mathematics
- 2017

Characteristic classes are invariants for principal bundles that take values in the cohomology of the base space. In the first part of this paper, we propose a uniform interpretation of arbitrary…

### The 2-Hilbert Space of a Prequantum Bundle Gerbe

- Mathematics
- 2016

We construct a prequantum 2-Hilbert space for any line bundle gerbe whose Dixmier-Douady class is torsion. Analogously to usual prequantisation, this 2-Hilbert space has the category of sections of…

### Atiyah sequence and Gauge transformations of a principal 2-bundle over a Lie groupoid

- MathematicsJournal of Geometry and Physics
- 2022

### A Higher Stacky Perspective on Chern–Simons Theory

- Physics
- 2015

The first part of this text is a gentle exposition of some basic constructions and results in the extended prequantum theory of Chern–Simons-type gauge field theories. We explain in some detail how…

### Central extensions of mapping class groups from characteristic classes

- Mathematics
- 2015

We characterize, for every higher smooth stack equipped with "tangential structure", the induced higher group extension of the geometric realization of its higher automorphism stack. We show that…

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