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Information × Registration Number 0213U001170, 0112U004670 , R & D reports Title Development of algebraic and analytical methods in noncomutative geomtry and topology popup.stage_title Head Sharko Volodymur Vasulyevich, Registration Date 21-01-2013 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) In terms of discrete additive functions on the category of projective modules a criterion for p-minimality of projective crossed chain complexes is established. The results are applied to calculate the second Morse number of smooth manifold with boundary. 2) We introduce the class of groups P and prove that it coincides with the class of groups which are fundamental groups of orbits of functions in f in F(M, P) with respect to the right action of the diffeomorphism group D(M) of a compact surface M. 3) The correspondence between a certain class of connected singular link diagrams and S-connected planar graphs is identified. With the singular graphs and planar S-graphs we get estimates of braid index and torsion of singular links. 4) It is proved that open light maps with radial pseudo attracting isolated connected components of a fully invariant components of wandering set are topologically equivalent if and only if their distinguishing graphs are equivalent. 5) The representation of Kaloujnine group K_2 in the full group of isometries of a regular (infinite, root) tree T_p is studied, also a complete description is obtained of an exact image of f_2(K_2) in the group of infinite unitriangular (down) matrices UT(2) over the field of two elements. 6) A flat map of the tree (finite or infinite) is defined. It is proved that for a certain class of trees an image of a flat map is a level set of pseudo-harmonic function. 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