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Information × Registration Number 0221U102701, 0116U000069 , R & D reports Title Algebraic and topological invariants of smooth mappings popup.stage_title Head Maksymenko Serhii I, Registration Date 08-02-2021 Organization Institute of Mathematics of the National Academy of Sciences of Ukraine popup.description2  Algebraic and topological invariants of various classes of smooth mappings between manifolds are investigated. Sufficient conditions are obtained under which a piecewise smooth function on the segment is topologically stable with respect to averages with a finite discrete measure. The topological and algebraic properties of groups of diffeomorphisms and homeomorphisms preserving different classes of foliations are studied. In particular, it is considered singular foliations by level sets of a smooth function on a compact surface, one-dimensional foliations with noncompact leaves on noncompact surfaces, and singular Morse-Bott foliations on manifolds. The canonical forms of many important classes of operators and matrices are obtained. The category of homotopy coalgebras and cobar- and bar- constructions between some curves of algebras and coalgebras is described. It is planned to continue these studies using the methods of algebraic, differential, infinite-dimensional topology, category theory, linear algebra and mathematical physics. Product Description popup.authors Lyubashenko Volodymyr V Maksymenko Sergiy I Polulyakh Eugene O Sergeichuk Vladimir V Soroka Yuliya Yu. Feshchenko Bogdan H popup.nrat_date 2021-02-08 Close