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Meander diagrams of knots and spatial graphs: proofs of generalized Jablan–Radovic conjectures
Topology and its Applications. 2020. Vol. 274. Article 107122.
Малютин А. В., Belousov Y.
Language:
English
Nozdrinov A., Починка А. И., Журнал Средневолжского математического общества 2023 Т. 25 № 1 С. 531–541
In this paper we consider gradient-like Morse-Smale diffeomorphisms defined on the three-dimensional sphere S 3 . For such diffeomorphisms, a complete invariant of topological conjugacy was obtained in the works of C. Bonatti, V. Grines, V. Medvedev, E. Pecu. It is an equivalence class of a set of homotopically non-trivially embedded tori and Klein bottles ...
Added: March 22, 2023
Pochinka O., Medvedev T. V., Working papers by Cornell University. Series math "arxiv.org" 2023 P. 1–15
In this paper we give a lower estimate for the number of critical points of the Lyapunov function for Pixton diffeomorphisms (i.e. Morse-Smale diffeomorphisms in dimension 3 whose chain recurrent set consists of four points: one source, one saddle and two sinks). Ch. Bonatti and V. Grines proved that the class of topological equivalence of ...
Added: January 9, 2023
Alexander Dunaykin, Vyacheslav Zhukov, Moscow Mathematical Journal 2022 Vol. 22 No. 1 P. 69–81
To a singular knot K with n double points, one can associate a chord
diagram with n chords. A chord diagram can also be understood as a 4regular graph endowed with an oriented Euler circuit. L. Traldi introduced
a polynomial invariant for such graphs, called a transition polynomial.
We specialize this polynomial to a multiplicative weight system, that ...
Added: November 10, 2020
Li M., Lei F., Li F. et al., Journal of Knot Theory and Its Ramifications 2018 Vol. 27 No. 9 P. 1–19
We present formulae for computing the Yamada polynomial of spatial graphs obtained by replacing edges of plane graphs, such as cycle-graphs, theta-graphs, and bouquet-graphs, by spatial parts. As a corollary, it is shown that zeros of Yamada polynomials of some series of spatial graphs are dense in a certain region in the complex plane, described ...
Added: October 28, 2020
Nozdrinova E., Russian Journal of Nonlinear Dynamics 2018 Vol. 14 No. 4 P. 543–551
The problem of the existence of a simple arc connecting two structurally stable systems on a closed manifold is included in the list of the fifty most important problems of dynamical systems. This problem was solved by S. Newhouse and M. Peixoto for Morse-Smale flows on an arbitrary closed manifold in 1980. As follows from ...
Added: November 8, 2018
Pochinka O., Nozdrinova E., Журнал Средневолжского математического общества 2018 Т. 20 № 1 С. 30–38
In this paper we consider a class Phi of diffeomorphisms of a closed n -dimensional manifold that are bifurcation points of simple arcs in the space of diffeomorphisms. The authors have studied the asymptotic properties and the embedding structure of invariant manifolds of non-wandering points of such diffeomorphisms. ...
Added: February 19, 2018
Markaryan N. S., Journal of Knot Theory and Its Ramifications 2016 Vol. 26 No. 12
Given a Lie algebra with a scalar product, one may consider the latter as a symplectic structure on a $dg$-scheme, which is the spectrum of the Chevalley--Eilenberg algebra. In the first section we explicitly calculate the first order deformation of the differential on the Hochschild complex of the Chevalley--Eilenberg algebra. The answer contains the Duflo ...
Added: February 10, 2016
Skopenkov M., International Journal of Mathematics 2015 Vol. 26 No. 7, Article number 1550051 P. 1–28
Given a manifold N and a number m, we study the following question: is the set of isotopy classes of embeddings N → Sm finite? In case when the manifold N is a sphere the answer was given by A. Haefliger in 1966. In case when the manifold N is a disjoint union of spheres the ...
Added: September 8, 2015
Pochinka O., Grines V., Mathematical notes 2013 Vol. 94 No. 6 P. 862–875
The results obtained in this paper are related to the Palis–Pugh problem on the existence of an arc withfinitely or countably many bifurcations which joins two Morse–Smale systems on a closed smooth manifoldMn . Newhouse and Peixoto showed that such an arc joining flows exists for any nand, moreover, it is simple. However, there exist ...
Added: September 11, 2014