Teorija dimenzij in geometrijska topologija (Slovene)

The object of our research will be numerous unsolved problems of contemporary topology. In general topology we shall investigate theory of continuous selections of multivalued mappings on Banach spaces and geometric aspects of (general and cohomological) dimension theory of compact metric spaces (mostly theory of general position for continuous maps into Euclidean spaces of higher dimensions. In algebraic topology we shall investigate theory of cohomological dimension over nonabelian groups (mostly in connection with the problem of rising dimension under cell-like mappings on topological 4-manifolds), actions by various classes of topological (e.g. Lie) groups on equivariant CW complexes, groups of homotopy auto-equivalences and the Hilbert-Smith conjecture for Riemannian manifolds (mostly generalizations from the Lipschitz-Hoelder case to the general case). In topological manifolds we shall investigate (homogeneous) wild Cantor sets in Euclidean spaces of dimensions 3 and 4 (mostly various forms of characterization of wild embeddings and various ambient homogeneities), theory of knots and links, obstruction theory for surgery on manifold pairs and questions from PL and DIFF topology. We shall also study integrable systems and Kac-Moody algebras. The proposed research is related to and continues the previous very successful investigations by this program group in this field and is also connected to the problems, which we are studying in several international projects run by this program group.