• Corpus ID: 223607712

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… 

TheR-local homotopy theory of smooth spaces

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

  • Severin Bunk
  • Mathematics
    Journal 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

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

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

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

References

SHOWING 1-10 OF 41 REFERENCES

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

Central extensions of smooth 2–groups and a finite-dimensional string 2–group

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

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

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

Loop Spaces, Characteristic Classes and Geometric Quantization

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

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

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

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