Nonlocal invariants in index theory

Details Nonlocal invariants in index theory Nonlocal invariants in index theory

1997-07-21

arxiv.org/abs/dg-ga/9707014v1

Mathematics

Differential Geometry

12 pages, Latex, also available at http://math.bu.edu/people/sr

Scientific paper

This article surveys the relations among local and nonlocal invariants in Atiyah-Singer index theory. We discuss the local invariants that arise from the heat equation approach to the index theorem for geometric operators, as well as the nonlocal invariants (the eta invariant, the determinant of the Laplacian/analytic torsion) that occur in more refined index theorems, such as the determinant line bundle setting and the index theorem for families of manifolds with boundary. We also discuss the higher torsion forms of Bismut and Lott and their conjectured relation to the rational homotopy of the diffeomorphism group of aspherical manifolds.

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