1 citations · 1 across the 10 of their papers we have counts for
10 papers
Linking invariants of spatial graphs
E. Alkin, Yu. Khromin, A. Skopenkov
We recall definitions of linking numbers and Wu--Simon numbers for spatial graphs. We expose a `converse' to the Conway--Gordon--Sachs theorem (i.e. description of linking function…
The winding number of a closed curve around a point
E. Alkin, A. Miroshnikov, A. Skopenkov
In this expository note we present an elementary direct rigorous definition and the simplest properties of the winding number. This definition is simpler than the one given in some…
Homotopy classification of closed polygonal lines
E. Alkin, O. Nikitenko, A. Skopenkov
In this text we expose basic cases of some fundamental ideas and methods of topology. Namely, of homotopy, degree, fundamental group, covering, Whitehead invariant, etc. This is do…
Low rank matrix completion and realization of graphs: results and problems
S. Dzhenzher, T. Garaev, O. Nikitenko +3
The Netflix problem (from machine learning) asks the following. Given a ratings matrix in which each entry represents the rating of movie by customer , if customer $…
Invariants of almost embeddings of graphs in the plane
E. Alkin, A. Miroshnikov, A. Skopenkov
A graph drawing in the plane is called an almost embedding if the images of any two non-adjacent simplices (i.e. vertices or edges) are disjoint. Almost embeddings (more precisely,…
Invariants of almost embeddings of graphs in the plane: results and problems
E. Alkin, E. Bordacheva, A. Miroshnikov +2
A graph drawing in the plane is called an almost embedding if images of any two non-adjacent simplices (i.e. vertices or edges) are disjoint. We introduce integer invariants of alm…
Cycles in graphs and in hypergraphs: towards homology theory
A. Miroshnikov, O. Nikitenko, A. Skopenkov
In this expository paper we present some ideas of algebraic topology (more precisely, of homology theory) in a language accessible to non-specialists in the area. A -cycle in a…
Cycles in graphs and in hypergraphs: results and problems
E. Alkin, S. Dzhenzher, O. Nikitenko +2
This is an expository paper. A -cycle in a graph is a set of edges such that every vertex is contained in an even number of edges from . E.g., a cycle in the sense of gra…
A quadratic estimation for the Kühnel conjecture on embeddings
S. Dzhenzher, A. Skopenkov
The classical Heawood inequality states that if the complete graph on vertices is embeddable in the sphere with handles, then . A higher-…
Embeddings of -complexes in -manifolds and minimum rank of partial symmetric matrices
A. Skopenkov
Let be a -dimensional simplicial complex having faces of dimension , and a closed -connected PL -dimensional manifold. We prove that for odd $K…