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Information × Registration Number 0213U001668, 0112U006696 , R & D reports Title Application of L^2 theory to symplectic topology popup.stage_title Head Sharko Vladimir Vasilievich, Registration Date 21-01-2013 Organization Institute of Mathematics of the National Academy of Sciences of Ukraine popup.description2 We study a bunch of actual problems of topology which can be utilized to solve problems of symplectic topology. Also we suggest applications of topological methods to qualitative theory of dynamical systems and complex analysis. In particular following problems are solved. 1) Investigated S^1-invariant vector fields on manifolds of even dimension with semisimple action of the circle with the finite number of fixed points p_1 , ... , p_2k. It is proved that on the manifold M^2k for every preassigned set of indexes lambda_1, ... , lambda_2k, 0 leq lambda_i leq 2n, there exists S^1-invariant Bott function with critical points p_1, ... , P_2k of indexes lambda_1, ... , lambda_2k. As a consequence, there is S^1-invariant Morse-Smale vector field V on M^2k with the state St_V ( lambda_i). We calculated the S^1-invariant Morse numbers M^nu_{S^1} (W^2n, St(0, r, 2n)). 2) Let X be a paracompact space and G be a subgroup of the group of homeomorphisms, which are finitely factorizable on the complement X setminus Fix G. We investigated properties of normal subgroups H of G, satisfying Fix (H) = Fix (G). 3) The research was conducted of regular components of two-dimensional open light maps and a topological classification was obtained of two-dimensional inner light maps on invariant regular component of wandering set with a special border. 4) Let T be a tree, finite or infinite, V_0 be a set of vertices of valence 1. We give a sufficient condition that a image of an embedding Psi: T setminus V_0 to R^2 was the level set of pseudo-harmonic function. 5) We solve the problem classifying pairs of linear maps A: V to W, B: W to V on unitary (or Euclidean) spaces V and W up to topological equivalence. Product Description popup.authors Власенко Ігор Юрійович Максименко Сергій Іванович Полулях Євген Олександрович Рибалкіна Тетяна Володимирівна popup.nrat_date 2020-04-02 Close