E. Alkin

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20242026

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math.HO2025

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…

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…

Homotopy classification of closed polygonal lines

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

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