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
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References
SHOWING 1-10 OF 41 REFERENCES
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…
Central extensions of smooth 2–groups and a finite-dimensional string 2–group
- Mathematics
- 2011
We provide a model of the String group as a central extension of finite-dimensional 2‐groups in the bicategory of Lie groupoids, left-principal bibundles, and bibundle maps. This bicategory is a…
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…
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…
Loop Spaces, Characteristic Classes and Geometric Quantization
- Mathematics
- 1994
This book deals with the differential geometry of manifolds, loop spaces, line bundles and groupoids, and the relations of this geometry to mathematical physics. Recent developments in mathematical…
Algebraic Structures for Bundle Gerbes and the Wess-Zumino Term in Conformal Field Theory
- Mathematics
- 2008
Surface holonomy of connections on abelian gerbes has essentially improved the geometric description of Wess-Zumino-Witten models. The theory of these connections also provides a possibility to…
From loop groups to 2-groups
- Mathematics
- 2005
We describe an interesting relation between Lie 2-algebras, the Kac– Moody central extensions of loop groups, and the group String(n). A Lie 2-algebra is a categorified version of a Lie algebra where…
Homological obstructions to string orientations
- Mathematics
- 2008
We observe that the Poincare duality isomorphism for a string manifold is an isomorphism of modules over the subalgebra A(2) of the modulo 2 Steenrod algebra. In particular, the pattern of the…