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The eta invariant and K0 of lens spaces. (English) Zbl 0597.58030

The eta invariant of Atiyah, Patodi, and Singer provides a family of R/Z valued invariants which completely detect the complex K-theory of odd dimensional lens spaces. The complexification map c: K0(M)\(\to K(M)\) is injective modulo 2-torsion. We refine the eta invariant using the reality condition to define invariants detecting Ker(c) and thereby define invariants completely detecting K0(M) for M an odd dimensional lens space.

MSC:

58J20 Index theory and related fixed-point theorems on manifolds
55R50 Stable classes of vector space bundles in algebraic topology and relations to \(K\)-theory
57R20 Characteristic classes and numbers in differential topology
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References:

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