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

Topological and homological properties of the orbit space of a simple three-dimensional compact linear Lie group