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The Eta-invariant and Pontryagin duality in K-theory | | A.Yu. Savin
; B.Yu. Sternin
; | | Date: |
6 Jun 2000 | | Journal: | Mathematical notes, v. 71, n. 2, 2002, 245-261. Translated from Matematicheskie Zametki v. 71, n. 2, 2002, 271-291 | | Subject: | K-Theory and Homology; Analysis of PDEs; Algebraic Topology; Differential Geometry; Operator Algebras; Spectral Theory MSC-class: 58J28, 19L64 (Primary); 58J22, 19K56, 58J40 (Secondary) | math.KT math.AP math.AT math.DG math.OA math.SP | | Affiliation: | Moscow State University), B.Yu. Sternin (Moscow State University | | Abstract: | The 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. | | Source: | arXiv, math.KT/0006046 | | Services: | Forum | Review | PDF | Favorites | |
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