Geodesic
The Eta-Invariant and Pontryagin Duality in $K$-Theory
Matematičeskie zametki, Tome 71 (2002) no. 2, pp. 271-291

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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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     author = {A. Yu. Savin and B. Yu. Sternin},
     title = {The {Eta-Invariant} and {Pontryagin} {Duality} in $K${-Theory}},
     journal = {Matemati\v{c}eskie zametki},
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     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2002_71_2_a10/}
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A. Yu. Savin; B. Yu. Sternin. The Eta-Invariant and Pontryagin Duality in $K$-Theory. Matematičeskie zametki, Tome 71 (2002) no. 2, pp. 271-291. http://geodesic.mathdoc.fr/item/MZM_2002_71_2_a10/