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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
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 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