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arXiv · 2308.07813

Maximal degree of a map of surfaces

Andrey Ryabichev
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Abstract

Given closed possibly nonorientable surfaces $M,N$, we prove that if a map $f:M\to N$ has degree $d>0$, then $\chi(M)\le d\cdot\chi(N)$. We give all necessary comments on the definition and properties of geometric degree, which can be defined for any map. Our proof is based on the Kneser-Edmonds factorization theorem, simple natural proof of which is also presented.

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Andrey Ryabichev. 2023-08-15. Maximal degree of a map of surfaces. https://doi.org/10.2140/pjm.2024.328.145

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