The d-invariant of compact nilmanifolds
type: Item
instance of: scholarly article
title: The d-invariant of compact nilmanifolds
zbMATH Open document ID: 0558.55009
DOI: 10.1007/BF01388717
published in: Inventiones Mathematicae
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143167
review text: Let G be a simply connected nilpotent Lie group and \(\Gamma\) a discrete subgroup such that G/\(\Gamma\) is compact. Then a choice of an orientation provides G/\(\Gamma\) with a stable framing. In this note it is shown that the Adams-d-invariant d[G/\(\Gamma\) ] vanishes (if dim G\(>2)\). The proof uses the relation of the d-invariant to the index of the Dirac operator; it proceeds by comparison through a sequence of discrete subgroups \(\Gamma_ i\) of G.
Mathematics Subject Classification ID: 55Q45
Mathematics Subject Classification ID: 55Q50
Mathematics Subject Classification ID: 58J20
Mathematics Subject Classification ID: 55R50
zbMATH DE Number: 3890356
zbMATH Keywords: framed manifolds
zbMATH Keywords: stable homotopy groups of spheres
zbMATH Keywords: simply connected nilpotent Lie group
zbMATH Keywords: Adams-d-invariant
zbMATH Keywords: index of the Dirac operator
author: Wilhelm Singhof
reviewed by: Erich Ossa
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3890356