The Eta-invariant and Pontryagin duality in K-theory

Details The Eta-invariant and Pontryagin duality in K-theory The Eta-invariant and Pontryagin duality in K-theory

2000-06-06

arxiv.org/abs/math/0006046v2

Mathematical notes, v. 71, n. 2, 2002, 245-261. Translated from Matematicheskie Zametki v. 71, n. 2, 2002, 271-291

Mathematics

K-Theory and Homology

24 pages, 1 figure; final version; see http://www.kluweronline.com/issn/0001-4346/contents

Scientific paper

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.

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