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Information × Registration Number 0211U007900, 0111U007038 , R & D reports Title Development of algebraic and analytical methods in noncomutative geomtry and topology popup.stage_title Head Sharko Volodymur Vasulyevich, Registration Date 19-10-2011 Organization Institute of Mathematics of the National Academy of Sciences of Ukraine popup.description2 Important types of functions, 1-forms, dynamical systems and diffeomorphisms were studied with the help of methods of differential, algebraic and homotopical topology. Specifically, following results were obtained . 1) Necessary and sufficient conditions of existance of $p$-minimal projective crossed chain complexes are proved in terms of discreete additive functions on the cathegory of projective modules. Results obtained are applied to calculate second Morse number of smooth manifold with boundary. 2) Several languages are established to study infinite-dimensional matrices over $Z_2$ ring. Method of complete description was specified for matrix images of representation of elements of self-similar groups which act on the binary tree $T_2$. 3) Combinatorical models of incompressible torii in interlacing complement in 3-dimensional space were studied. Also geometric properties of tiled torii of standard position were obtained. 4) On the certain class of compact surfaces orbits of Morse functions with respect to right actions of automorphisms fixed on a prescribed open-close subset were explored. The results specified can be applied in research activities held in Kyiv, Kharkov, Lviv National universities and in Kharkov low temperature institute of NAS of Ukraine. Product Description popup.authors Власенко Ігор Юрійович Леонов Юрій Григорович Максименко Сергій Іванович Плахта Леонід Петрович Полулях Євген Олександрович Самойленко Анатолій Михайлович popup.nrat_date 2020-04-02 Close