Geometry & Topology

On the topological contents of $\eta$–invariants

Ulrich Bunke

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.

Article information

Source
Geom. Topol., Volume 21, Number 3 (2017), 1285-1385.

Dates
Revised: 20 May 2016
Accepted: 5 September 2016
First available in Project Euclid: 16 November 2017

https://projecteuclid.org/euclid.gt/1510859204

Digital Object Identifier
doi:10.2140/gt.2017.21.1285

Mathematical Reviews number (MathSciNet)
MR3650076

Zentralblatt MATH identifier
1370.58012

Subjects
Primary: 58J28: Eta-invariants, Chern-Simons invariants

Keywords
eta invariant $K$–theory bordism

Citation

Bunke, Ulrich. On the topological contents of $\eta$–invariants. Geom. Topol. 21 (2017), no. 3, 1285--1385. doi:10.2140/gt.2017.21.1285. https://projecteuclid.org/euclid.gt/1510859204

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