arXiv subjects

Danny Stevenson

Publications and source records attributed to Danny Stevenson.

23 records · Page 2Linked to original sources

arXiv2005

Entire cyclic homology of continuous trace algebras

A central result here is the computation of the entire cyclic homology of canonical smooth subalgebras of stable continuous trace C*-algebras having smooth manifolds M as their spectrum. More precisely, the entire cyclic homology is shown to be canonically isomorphic to the continuous periodic cyclic homology for these algebras. By an earlier result of the authors, one concludes that the entire cyclic homology of the algebra is canonically isomorphic to the twisted de Rham cohomology of M.

math.KT↗

arXiv2004

On a generalized Connes-Hochschild-Kostant-Rosenberg theorem

The central result here is an explicit computation of the Hochschild and cyclic homologies of a natural smooth subalgebra of stable continuous trace algebras having smooth manifolds X as their spectrum. More precisely, the Hochschild homology is identified with the space of differential forms on X, and the periodic cyclic homology with the twisted de Rham cohomology of X, thereby generalizing some fundamental results of Connes and Hochschild-Kostant-Rosenberg. The Connes-Chern character is also identified here with the twisted Chern character.

math.KT↗

arXiv2003

Chern character in twisted K-theory: equivariant and holomorphic cases

It has been argued by Witten and others that in the presence of a nontrivial B-field, D-brane charges in type IIB string theories are measured by twisted K-theory. In joint work with Bouwknegt, Carey and Murray it was proved that twisted K-theory is canonically isomorphic to bundle gerbe K-theory, whose elements are ordinary vector bundles on a principal projective unitary bundle, with an action of the bundle gerbe determined by the principal projective unitary bundle. The principal projective unitary bundle is in turn determined by the twist. In this paper, we study in more detail the Chern-Weil representative of the Chern character of bundle gerbe K-theory that was introduced previously, and we also extend it to the equivariant and holomorphic cases. Included is a discussion of interesting examples.

hep-th↗

arXiv2001

Bundle 2-gerbes

We make the category BGrb_M 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 BGrb_M as a 2-category is used to define the notion of a bundle 2-gerbe. To every bundle 2-gerbe on M is associated a class in H^4(M;Z). We define the notion of a bundle 2-gerbe connection and show how this leads to a closed, integral differential 4-form on M which represents the image in real cohomology of the class in H^4(M;Z). Some examples of bundle 2-gerbes are discussed, including the bundle 2-gerbe associated to a principal G-bundle P \to M. It is shown that the class in H^4(M;Z) associated to this bundle 2-gerbe coincides with the first Pontryagin class of P --- this example was previously considered from the point of view of 2-gerbes by Brylinski and McLaughlin.

math.DG↗

arXiv2000

The Geometry of Bundle Gerbes

This thesis reviews the theory of bundle gerbes and then examines the higher dimensional notion of a bundle 2-gerbe. The notion of a bundle 2-gerbe connection and 2-curving are introduced and it is shown that there is a class in $H^{4}(M;\Z)$ associated to any bundle 2-gerbe.

math.DG↗