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On the topological contents of η–invariants

Bunke, Ulrich


We discuss a universal bordism invariant obtained from the Atiyah-Patodi-Singer eta-invariant from the analytic and homotopy-theoretic point of view. Classical invariants like the Adams e-invariant, rho-invariants and String-bordism invariants are derived as special cases. The main results are a secondary index theorem about the coincidence of the analytic and topological constructions and intrinsic expressions for the bordism invariants.

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