On quasicompact homogeneous spaces (Q350844)

The author studies quasicompact homogeneous spaces \(M = G/H\), i.e., homogeneous spaces which admit a finite invariant measure, and gives a description of such manifolds of a connected Lie group \(G\) up to finite coverings. In particular, he proves that a finite covering of \( M\) has a representation as a homogeneous space \(M' = G'/H'\) such that \(G'= N_{G'}(H_0)\cdot S'_c\), where \(N_{G'}(H_0)\) is the normalizer of the connected component of \(H\) and \(S'_c\) is the compact factor of a Levi subgroup of \(G'\). He gives a more detailed description of a quasicompact homogeneous manifold \(M =G/H\) such that \(G\) is a minimal transitive subgroup, i.e., there is no proper transitive subgroup of \(G\). A classification of all quasicompact homogeneous manifolds of dimension \(n \leq 6\) is obtained. The author also studies the fundamental group of a quasicompact manifold and describes its structure up to a weak commensurability.