Compact homogeneous spaces with a semisimple fundamental group. II
[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.
fundamental group of a compact homogeneous space
diffeomorphic, up to a finite-leaved covering
scientific article; zbMATH DE number 4050553