E. Alkin

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20222026

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4 papers · 1 filter

math.GT2026

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…

math.GT2025

On winding numbers of almost embeddings of $K_{4}$ in the plane

Emil Alkin, Alexander Miroshnikov

Let $K_{4}$ be the complete graph on four vertices. Let $f$ be a continuous map of $K_{4}$ to the plane such that $f$ -images of non-adjacent edges are disjoint. For any vertex $v \in K…

math.GT2024

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,…

math.GT2022

Hardness of almost embedding simplicial complexes in $R^{d}$ , II

Emil Alkin

A map $f : K \to R^{d}$ of a simplicial complex is an almost embedding if $f (σ) \cap f (τ) = \emptyset$ whenever $σ, τ$ are disjoint simplices of $K$ . Fix integers $d,k \geq…

Linking invariants of spatial graphs

On winding numbers of almost embeddings of K4​ in the plane

Invariants of almost embeddings of graphs in the plane

Hardness of almost embedding simplicial complexes in Rd, II

On winding numbers of almost embeddings of $K_{4}$ in the plane

Hardness of almost embedding simplicial complexes in $R^{d}$ , II