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Information × Registration Number 0212U001645, 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 16-02-2012 Organization Institute of Mathematics of the National Academy of Sciences of Ukraine popup.description2 A number of current problems of topology is investigated, also applications of topological methods to the qualitative theory of dynamical systems and algebra are proposed. In particular, the following problems are solved. 1) In terms of discrete additive functions on the cathegory of projective modules we prove necessary and sufficient conditions of the existance of $p$-minimal projective crossed chain complexes. Results obtained are used to calculate second Morse number of smooth manifold with boundary. 2) Orbits of Morse functions on a certain class of compact surfaces with respect to right actions of automprphisms of surfaces stationary on a fixed open-closed subset were investigated. 3) With the help of technique of automorphism factorizable subgroups we examined the structure of normal subgroups preserving fibers of a certain foliation $F$ on $M$ of an arbitrary smooth manifold $M$ diffeomorphisms group. 4) Several languages of studying of infinite dimensional matrices over the ring $Z_2$ are established. Method of full description of matrix images of self-similar groups on a binary tree $T-2$ elements representation is specified. 5) Full description of images of Kaluzshnin group elements in the group of lower unitriangle matrices is given. 6) We investigated combinatorial models of incompressible tori in a wreath complement in 3-dimentional space. Also we investigated geometrical properties of tiled tori in the standard position. 7) The estimate of braid index of wreaths conforming with $S$-graphs which have two component totally colored subgraphs was improved. 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