The Eta-invariant and Pontryagin duality in K-theory

A. Yu. Savin; B. Yu. Sternin

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arXiv · math/0006046

The Eta-invariant and Pontryagin duality in K-theory

A. Yu. Savin·B. Yu. Sternin

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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.

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BibTeX RIS

A. Yu. Savin, B. Yu. Sternin. 2002-07-20. The Eta-invariant and Pontryagin duality in K-theory. https://arxiv.org/abs/math/0006046

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