Minimal dimensions for flat manifolds with prescribed holonomy
type: Item
instance of: scholarly article
title: Minimal dimensions for flat manifolds with prescribed holonomy
zbMATH Open document ID: 0648.57017
DOI: 10.1007/BF01442498
author: Wilhelm Plesken
published in: Mathematische Annalen
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164566
review text: The paper develops some general methods to find the minimal dimensions of compact connected flat Riemannian manifolds with given isomorphism class for its holonomy group or equivalently the minimal dimension of a fixed point free crystallographic space group with given isomorphism type for its point group. The methods are based on the investigation of the p-adic completions of the space groups involved and are made quite explicit for point groups having cyclic Sylow subgroups for some primes. Since the method can be used for many perfect groups it extends the range of earlier work by various authors on the problem for soluble groups. The results are applied to find these minimal dimensions for \(PSL_ 2(p)\) and \(SL_ 2(p)\).
Mathematics Subject Classification ID: 57S30
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 20H15
Mathematics Subject Classification ID: 51F15
zbMATH DE Number: 4058453
zbMATH Keywords: minimal dimensions of compact connected flat Riemannian manifolds with given holonomy group
zbMATH Keywords: fixed point free crystallographic space group
zbMATH Keywords: p- adic completions of the space groups
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4058453