Search academic texts

Information × Registration Number 0213U001171, 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) S^1 Bott maps in a circle and a straight line were studied. In particular, we examined S^1-invariant maps of smooth manifolds with circle action. 2) The necessary and sufficient conditions are found for a group S_id (f, X) (the connected component of the identity mapping in the stabilizer of f under the right action of the diffeomorphism group D (M) on the space of smooth functions on M) to be homotopy equivalent to a circle. 3) New results are obtained on the stability of braid index of knots and links with respect to insertions of k-torsions into a chart, the properties of reduction operations on classical and singular links and corresponding Seifert graphs and S-graphs, as well as their connection with several well-known conjectures in knot theory is established. 4) Investigated regular components of two-dimensional maps of ineer light maps on invariant regular component of wandering sets. It is shown that in general the number of classes of topological conjugacy of contraction of an inner light map on its wandering set is infinite. 5) Studied matrix representation f_2 images of self-similar groups that are subgroups K_2. 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