The computation of \(\eta\)-invariants on manifolds with free circle action
type: Item
instance of: scholarly article
title: The computation of \(\eta\)-invariants on manifolds with free circle action
zbMATH Open document ID: 1026.53025
author: S. Bechtluft-Sachs
published in: Journal of Functional Analysis
publication date: 2003-04-06T00:00:00Z
review text: In this paper the author considers a Riemannian spin-manifold \(M\) of positive scalar curvature carrying a free and isometric circle action of the circle \({\mathbf S}^1\) with geodesic orbits. He explicitly computes the \(\eta\)-invariant of twisted Dirac operators on \(M\), by a computation which is based upon the index theorem. As a first application he lists the explicit result for the (generalized) Berger spheres of dimension less than or equal to 11, and as a second application he derives a formula for the adiabatic limit of \(\eta\)-invariants.
reviewed by: Alberto Parmeggiani
Mathematics Subject Classification ID: 53C27
Mathematics Subject Classification ID: 58J28
zbMATH DE Number: 1496040
zbMATH Keywords: spin-manifolds
zbMATH Keywords: Dirac operators
zbMATH Keywords: \(\eta\)-invariants
zbMATH Keywords: circle action
MaRDI profile type: Publication
full work available at URL: jfan.2000.3584
OpenAlex ID: W2076758349
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DOI: 10.1006/JFAN.2000.3584
description: scientific article; zbMATH DE number 1496040