• Corpus ID: 199687856

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… 
ncatlab.org
80 Citations
Highly Influential Citations
6
Background Citations
28
Methods Citations
7
Results Citations
1

80 Citations

Principal ∞-Bundles and Smooth String Group Models

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

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

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

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

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

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

Extended higher cup-Product Chern-Simons theories

A Higher Stacky Perspective on Chern–Simons Theory

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

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…
...

References

SHOWING 1-10 OF 61 REFERENCES

Principal ∞-bundles : presentations

We discuss two aspects of the presentation of the theory of principal ∞-bundles in an ∞-topos, introduced in Nikolaus et al. (Principal ∞-bundles: general theory, 2012), in terms of categories of…

Lifting Problems and Transgression for Non-Abelian Gerbes

Homotopical algebraic geometry. I. Topos theory.

Classification of extensions of principal bundles and transitive Lie groupoids with prescribed kernel and cokernel

The equivalence of principal bundles with transitive Lie groupoids due to Ehresmann is a well-known result. A remarkable generalization of this equivalence, given by Mackenzie, is the equivalence of…

Twisted Differential String and Fivebrane Structures

In the background effective field theory of heterotic string theory, the Green-Schwarz anomaly cancellation mechanism plays a key role. Here we reinterpret it and its magnetic dual version in terms…

Bundle 2‐gerbes

We make the category BGrbM 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 BGrbM as a 2‐category…

Twists of K-theory and TMF

We explore an approach to twisted generalized cohomology from the point of view of stable homotopy theory and quasicategory theory provided by arXiv:0810.4535. We explain the relationship to the…

On the classification of fibrations

This thesis consists of two articles. Both articles concern homotopical algebra. In Paper I we study functors indexed by a small category into a model category whose value at each morphism is a weak…

Twisted K-Theory and K-Theory of Bundle Gerbes

Abstract: In this note we introduce the notion of bundle gerbe K-theory and investigate the relation to twisted K-theory. We provide some examples. Possible applications of bundle gerbe K-theory to…

Segal topoi and stacks over Segal categories

In math.AG/0207028 we began the study of higher sheaf theory (i.e. stacks theory) on higher categories endowed with a suitable notion of topology: precisely, we defined the notions of S-site and of…
...