The Eta-invariant and Pontryagin duality in K-theory

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dc.creatorSavin, A. Yu.
dc.creatorSternin, B. Yu.
dc.date2000-06-06
dc.date2002-07-20
dc.date.accessioned2026-07-07T04:35:45Z
dc.date.available2026-07-07T04:35:45Z
dc.descriptionThe 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.
dc.description24 pages, 1 figure; final version; see http://www.kluweronline.com/issn/0001-4346/contents
dc.identifierhttps://arxiv.org/abs/math/0006046
dc.identifierhttp://arxiv.org/abs/math/0006046
dc.identifierMathematical notes, v. 71, n. 2, 2002, 245-261. Translated from Matematicheskie Zametki v. 71, n. 2, 2002, 271-291
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/59362
dc.subjectK-Theory and Homology
dc.subjectAnalysis of PDEs
dc.subjectAlgebraic Topology
dc.subjectDifferential Geometry
dc.subjectOperator Algebras
dc.subjectSpectral Theory
dc.subject58J28, 19L64 (Primary); 58J22, 19K56, 58J40 (Secondary)
dc.titleThe Eta-invariant and Pontryagin duality in K-theory
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