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Mathematical Notes

, Volume 71, Issue 1–2, pp 245–261 | Cite as

The Eta-Invariant and Pontryagin Duality in K-Theory

  • A. Yu. Savin
  • B. Yu. Sternin
Article

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.

eta-invariant K-theory Pontryagin duality linking coefficients Atiyah--Patodi--Singer theory modulo n index 

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Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • A. Yu. Savin
    • 1
  • B. Yu. Sternin
    • 1
  1. 1.M. V. Lomonosov Moscow State UniversityRussia

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