Higher-Degree Analogs of the Determinant Line Bundle |
| |
Authors: | John Lott |
| |
Institution: | (1) Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1109, USA. E-mail:lott@umich.edu , US |
| |
Abstract: | In the first part of this paper, given a smooth family of Dirac-type operators on an odd-dimensional closed manifold, we
construct an abelian gerbe-with-connection whose curvature is the three-form component of the Atiyah-Singer families index
theorem. In the second part of the paper, given a smooth family of Dirac-type operators whose index lies in the subspace of the reduced K-theory of the parametrizing space, we construct a set of Deligne cohomology classes of degree i whose curvatures are the i-form component of the Atiyah-Singer families index theorem.
Received: 27 September 2001 / Accepted: 5 April 2002 Published online: 22 August 2002 |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|