Maximal degree of a map of surfaces
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866914755960111104 |
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| author | Ryabichev, Andrey |
| author_facet | Ryabichev, Andrey |
| contents | Given closed possibly nonorientable surfaces $M,N$, we prove that if a map $f:M\to N$ has degree $d>0$, then $χ(M)\le d\cdotχ(N)$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_07813 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Maximal degree of a map of surfaces Ryabichev, Andrey Geometric Topology Given closed possibly nonorientable surfaces $M,N$, we prove that if a map $f:M\to N$ has degree $d>0$, then $χ(M)\le d\cdotχ(N)$. 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. |
| title | Maximal degree of a map of surfaces |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2308.07813 |