Do almost flat manifolds bound?
type: Item
instance of: scholarly article
title: Do almost flat manifolds bound?
zbMATH Open document ID: 0543.53037
author: Smilka Zdravkovska
author: F. Thomas Farrell
published in: Michigan Mathematical Journal
publication date: 1983-01-01T00:00:00Z
review text: The long standing conjecture that flat manifolds bound was proved by \textit{G. C. Hamrick} and \textit{D. C. Royster} [Invent. Math. 66, 405-413 (1982; Zbl 0476.57018]. The present authors take up the interesting problem whether the same thing holds for almost flat manifolds in the sense of \textit{M. Gromov} [J. Differ. Geom. 13, 231-241 (1978; Zbl 0432.53020)]. Their main result is that this is indeed the case if the fundamental group \(\pi_ 1(M)\) of the almost flat manifold M contains a nilpotent subgroup of index either m or 2m, where m is an odd integer.
reviewed by: Karsten Grove
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 57S30
Mathematics Subject Classification ID: 57R99
zbMATH DE Number: 3864034
zbMATH Keywords: almost flat manifolds
zbMATH Keywords: fundamental group
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1029002850
OpenAlex ID: W2032388815
DOI: 10.1307/MMJ/1029002850
description: scientific article; zbMATH DE number 3864034