Kolesnyk P. Application of matrix problems to the problems in stable homotopy theory

Dissertation researches and classifies objects of the stable homotopy category - finite cell complexes (polyhedra), and algebraic structures generated by polyhedra. New approach to the stable homotopy classification was applied in order to solve this problem: it seems more "algebraic" and easy for computations. This approach utilizes triangulated structure of stable homotopy category and technique of matrix problems for obtaining local classification. New approach also made it possible to apply techniques developed for genera of integer representations to the research on genera of polyhedra, and to obtain global classification of objects of stable homotopy category.