#### Volume 21, issue 3 (2017)

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On the topological contents of $\eta$–invariants

### Ulrich Bunke

Geometry & Topology 21 (2017) 1285–1385
##### Abstract

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.

##### Keywords
eta invariant, $K$–theory, bordism
Primary: 58J28
##### Publication
Received: 8 November 2013
Revised: 20 May 2016
Accepted: 5 September 2016
Published: 10 May 2017
Proposed: Ralph Cohen
Seconded: Peter Teichner, Tomasz Mrowka
##### Authors
 Ulrich Bunke Fakultät für Mathematik Universität Regensburg D-93040 Regensburg Germany