The Eta-Invariant and Pontryagin Duality in $K$-Theory

A. Yu. Savin ; B. Yu. Sternin

Matematičeskie zametki, Tome 71 (2002) no. 2, pp. 271-291.

Résumé

The topological significance of the spectral Atiyah–Patodi–Singer $\eta$-invariant is investigated. 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. Pontryagin duality implies the nondegeneracy of the linking form. An example of a nontrivial fractional part for an even-order operator is presented.

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