7 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…
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…
On winding numbers of almost embeddings of in the plane
Emil Alkin, Alexander Miroshnikov
Let be the complete graph on four vertices. Let be a continuous map of to the plane such that -images of non-adjacent edges are disjoint. For any vertex $v \in K…
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: 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…
Hardness of almost embedding simplicial complexes in , II
Emil Alkin
A map of a simplicial complex is an almost embedding if whenever are disjoint simplices of . Fix integers $d,k \geq…