On the topological contents of η–invariants

Bunke, Ulrich

doi:10.2140/gt.2017.21.1285

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On the topological contents of $\eta$–invariants

Ulrich Bunke

Geometry & Topology 21 (2017) 1285–1385

DOI: 10.2140/gt.2017.21.1285

Abstract

We discuss a universal bordism invariant obtained from the Atiyah–Patodi–Singer $η$ –invariant from the analytic and homotopy-theoretic point of view. Classical invariants like the Adams $e$ –invariant, $ρ$ –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

Mathematical Subject Classification 2010

Primary: 58J28

References

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

Volume 21, issue 3 (2017)