The eta invariant and K0 of lens spaces (Q1079265)

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.