A. Ryabichev

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20212024

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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…