Scott Wilson: Chern-Simons forms, Free Loop Spaces, and K-theory скачать в хорошем качестве

Scott Wilson: Chern-Simons forms, Free Loop Spaces, and K-theory

Scott Wilson, City University of New York Abstract: A Chern-Simons form, associated to a path of connections on a bundle, is in fact the shadow of a certain equivariant form on the free loop space of the base. The latter mediates between Bismut-Chern forms, whose role in low dimensional TFT's has been explained by Han, Stolz and Teichner. In this talk, I'll describe how such differential forms on the free loop space provide a geometric refinement of Chern- Weil theory, as well as a geometric refinement of differential K-theory which contains holonomy information in its classes. This is joint work with Thomas Tradler and Mahmoud Zeinalian.