  The article is devoted to the question whether the orbit space of a compact
linear group is a topological manifold and a homological manifold. In the
paper, the case of a simple three-dimensional group is considered. An upper
bound is obtained for the sum of the half-dimension integral parts of the
irreducible components of a representation whose quotient space is a
homological manifold, that enhances an earlier result giving the same bound if
the quotient space of a representation is a smooth manifold. The most of the
representations satisfying this bound are also researched before. In the
proofs, standard arguments from linear algebra, theory of Lie groups and
algebras and their representations are used.
