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Mat. Zametki, 2002, Volume 71, Issue 2, Pages 271–291 (Mi mz346)  

This article is cited in 3 scientific papers (total in 3 papers)

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

A. Yu. Savin, B. Yu. Sternin

M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

Abstract: 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.

DOI: https://doi.org/10.4213/mzm346

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English version:
Mathematical Notes, 2002, 71:2, 245–261

Bibliographic databases:

UDC: 517.9
Received: 25.04.2001

Citation: A. Yu. Savin, B. Yu. Sternin, “The Eta-Invariant and Pontryagin Duality in $K$-Theory”, Mat. Zametki, 71:2 (2002), 271–291; Math. Notes, 71:2 (2002), 245–261

Citation in format AMSBIB
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\paper The Eta-Invariant and Pontryagin Duality in $K$-Theory
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  • https://doi.org/10.4213/mzm346
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Savin A., Sternin B., “The eta invariant and parity conditions”, Adv. Math., 182:2 (2004), 173–203  crossref  mathscinet  zmath  isi
    2. Savin A., Sternin B., “Pseudo Differential Subspaces and their Applications in Elliptic Theory”, C(Star)-Algebras and Elliptic Theory, Trends in Mathematics, eds. Bojarski B., Mishchenko A., Troitsky E., Weber A., Birkhauser Boston, 2006, 247–289  crossref  mathscinet  zmath  isi
    3. Warren A.R., “The K-Theoretic Formulation of D-Brane Aharonov-Bohm Phases”, Adv. High. Energy Phys., 2012, 920486  crossref  mathscinet  zmath  isi  elib
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