Compact homogeneous spaces with a semisimple fundamental group. II
type: Item
instance of: scholarly article
title: Compact homogeneous spaces with a semisimple fundamental group. II
zbMATH Open document ID: 0644.57006
DOI: 10.1007/BF00969194
author: V. V. Gorbatsevich
published in: Siberian Mathematical Journal
publication date: 1986-01-01T00:00:00Z
review text: [For part I see Sib. Mat. Zh. 22, No.1, 47-67 (1981; Zbl 0486.57019)]. After proving a characterization showing when a semi-simple group is the fundamental group of a compact homogeneous space, this paper then goes on to study the natural fibration \(M_ c\to M\to M_ a\) for such a space. For example, it is shown that if M is a compact homogeneous semi-simple (i.e. the fundamental group is semi-simple) manifold, and \(M_ c\) has universal cover \(S^ n\), then \(n=3\), \(M_ a\) is an orientable surface \(F_ g\) of genus \(>1\) and M is diffeomorphic, up to a finite-leaved covering, to \(S^ 3\times F_ g\). It is also shown that there are principal fibrations whose properties are very close to those of the natural fibrations yet the principal fibrations do not correspond to manifolds.
Mathematics Subject Classification ID: 57N15
Mathematics Subject Classification ID: 53C30
Mathematics Subject Classification ID: 55R10
Mathematics Subject Classification ID: 57P99
zbMATH DE Number: 4050553
zbMATH Keywords: semi-simple group
zbMATH Keywords: fundamental group of a compact homogeneous space
zbMATH Keywords: universal cover
zbMATH Keywords: diffeomorphic, up to a finite-leaved covering
zbMATH Keywords: principal fibrations
zbMATH Keywords: natural fibrations
reviewed by: David B. Gauld
MaRDI profile type: Publication
cites work: Q3946826
cites work: Q5603082
cites work: Q3954539
full work available at URL: https://doi.org/10.1007/bf00969194
OpenAlex ID: W4247141255
description: scientific article; zbMATH DE number 4050553