A. Ryabichev

activity

20212024

collaborators

3 papers

math.GT2024

Short proof of the Kneser-Edmonds theorem on the degree of a map between closed surfaces

Andrey Ryabichev

Suppose for closed surfaces $M, N$ there exists a continuous map $f : M \to N$ of geometric degree $d > 0$ . Then $χ (M) \leq d \cdot χ (N)$ . This inequality was first proved by Kneser in case…

math.GT2023

Maximal degree of a map of surfaces

Andrey Ryabichev

Given closed possibly nonorientable surfaces $M, N$ , we prove that if a map $f : M \to N$ has degree $d > 0$ , then $χ (M) \leq d \cdot χ (N)$ . We give all necessary comments on the definition…

math.MG2021

Cutting a triangle into equal triangles

Andrey Ryabichev

We prove that almost every triangle can be dissected only into $n^{2}$ triangles which have to be equal one another. Moreover, such a dissection is unique for every $n$ . It turns out…