A Hilbert bundle description of differential Ktheory
Abstract
We give an infinite dimensional description of the differential Ktheory of a manifold $M$. The generators are triples $[H, A, \omega]$ where $H$ is a ${\bf Z}_2$graded Hilbert bundle on $M$, $A$ is a superconnection on $H$ and $\omega$ is a differential form on $M$. The relations involve eta forms. We show that the ensuing group is the differential Kgroup $\check{K}^0(M)$. In addition, we construct the pushforward of a finite dimensional cocycle under a proper submersion with a Riemannian structure. We give the analogous description of the odd differential Kgroup $\check{K}^1(M)$. Finally, we give a model for twisted differential Ktheory.
 Publication:

arXiv eprints
 Pub Date:
 December 2015
 arXiv:
 arXiv:1512.07185
 Bibcode:
 2015arXiv151207185G
 Keywords:

 Mathematics  Differential Geometry
 EPrint:
 final version, 52 pages