Veranstaltung

Vortrag
Sections and fibre integration in Deligne cohomology
Christian Becker (Potsdam)
8.5.2007, 14:00 Uhr – 15:00 Uhr

In classical U(1) gauge theories, the potentials are local 1-forms, which transform naturally under gauge transformations, whereas the field strength is a globally defined 2-form. In geometric terms, those data are described as connections and curvature in principal U(1)-bundles. Deligne cohomology classes generalize isomorphism classes of U(1) bundles with connection to objects, which are given locally as differential forms of higher degree. Those forms appear in string theory, e.g. as the B-field or even higher form fields. We discuss a notion of sections in Deligne cohomology classes.

In the talk we discuss a notion of sections for Deligne cohomology classes. We further discuss different approaches to a notion of intergration along the fibre for Deligne cohomology classes. This is of interest for the construction of transgression maps (which yield line isomorphism classes of line bundles on loop space from degree 2 Deligne cohomology classes) and topological quantum field theories in the sense of Atiyah.

Verknüpft mit:

• Christian Becker