The Eta-invariant and Pontryagin duality in K-theory
K-Theory and Homology
2007-05-23 v2 Analysis of PDEs
Algebraic Topology
Differential Geometry
Operator Algebras
Spectral Theory
Abstract
The topological significance of the spectral Atiyah-Patodi-Singer eta-invariant is investigated under the parity conditions of P. Gilkey. We show that twice the fractional part of the invariant is computed by the linking pairing in K-theory with the orientation bundle of the manifold. The Pontrjagin duality implies the nondegeneracy of the linking form. An example of a nontrivial fractional part for an even-order operator is presented. This result answers the question of P. Gilkey (1989) concerning the existence of even-order operators on odd-dimensional manifolds with nontrivial fractional part of eta-invariant.
Keywords
Cite
@article{arxiv.math/0006046,
title = {The Eta-invariant and Pontryagin duality in K-theory},
author = {A. Yu. Savin and B. Yu. Sternin},
journal= {arXiv preprint arXiv:math/0006046},
year = {2007}
}
Comments
24 pages, 1 figure; final version; see http://www.kluweronline.com/issn/0001-4346/contents