Affordable Access

Higher-Degree Analogs of the Determinant Line Bundle

Authors
Journal
Communications in Mathematical Physics
0010-3616
Publisher
Springer-Verlag
Publication Date
Disciplines
  • Mathematics

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.

There are no comments yet on this publication. Be the first to share your thoughts.