Corpus ID: 235605953

2-vector bundles

@inproceedings{Kristel20212vectorB,
  title={2-vector bundles},
  author={P. Kristel and Matthias Ludewig and K. Waldorf},
  year={2021}
}
We develop a ready-to-use comprehensive theory for (super) 2-vector bundles over smooth manifolds. It is based on the bicategory of (super) algebras, bimodules, and intertwiners as a model for 2-vector spaces. We show that our 2-vector bundles form a symmetric monoidal 2-stack, we discuss the dualizable, fully dualizable, and invertible objects, and we derive a classification in terms of non-abelian Cech cohomology. One important feature of our 2-vector bundles is that they contain bundle… Expand

Figures from this paper

References

SHOWING 1-10 OF 43 REFERENCES
Equivariance In Higher Geometry
We study (pre-)sheaves in bicategories on geometric categories: smooth manifolds, manifolds with a Lie group action and Lie groupoids. We present three main results: we describe equivariant descent,Expand
Topology, Geometry and Quantum Field Theory: Two-vector bundles and forms of elliptic cohomology
In this paper we define 2-vector bundles as suitable bundles of 2-vector spaces over a base space, and compare the resulting 2-K-theory with the algebraic K-theory spectrum K(V) of the 2-category ofExpand
Many finite-dimensional lifting bundle gerbes are torsion
Many bundle gerbes constructed in practice are either infinite-dimensional, or finite-dimensional but built using submersions that are far from being fibre bundles. Murray and Stevenson proved thatExpand
Twisted K-theory with coefficients in C*-algebras
We introduce a twisted version of $K$-theory with coefficients in a $C^*$-algebra $A$, where the twist is given by a new kind of gerbe, which we call Morita bundle gerbe. We use the description ofExpand
More morphisms between bundle gerbes.
Usually bundle gerbes are considered as objects of a 2-groupoid, whose 1- morphisms, called stable isomorphisms, are all invertible. I introduce new 1-morphisms which include stable isomorphisms,Expand
A künneth formula for the cyclic cohomology of ℤ/2-graded algebras
We define here Hochschild and cyclic (co)homology groups for Z/2-graded algebras. A definition of cyclic cohomology of such algebras over the complex numbers has already be given by Kastler [13-1 whoExpand
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 toExpand
Bundle gerbes
Just as C principal bundles provide a geometric realisation of two-dimensional integral cohomology; gerbes or sheaves of groupoids, provide a geometric realisation of three dimensional integralExpand
The Classification of Two-Dimensional Extended Topological Field Theories
We provide a complete generators and relations presentation of the 2-dimensional extended unoriented and oriented bordism bicategories as symmetric monoidal bicategories. Thereby we classify theseExpand
Loop groups and twisted K-theory I
This is the first in a series of papers investigating the relationship between the twisted equivariant K-theory of a compact Lie group G and the “Verlinde ring” of its loop group. In this paper weExpand
...
1
2
3
4
5
...