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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2501.18759 |
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| _version_ | 1866913709520060416 |
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| author | Amram, Meirav Chitayat, Michael Kopeliovich, Yaacov |
| author_facet | Amram, Meirav Chitayat, Michael Kopeliovich, Yaacov |
| contents | Let $X$ be a compact Riemann surface of genus $g$ and let $x \in X$. We derive the classical presentation of $π_1(X,x)$ (i.e the one given by $2g$ generators $a_1,b_1, \dots, a_g,b_g$ and the relation $\prod_{i=1}^g[a_i,b_i] = 1$)
from the description of $X$ as a branched cover $f : X \to \mathbb{C}\mathbb{P}^1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_18759 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Fundamental Group of a Compact Riemann Surface via Branched Covers Amram, Meirav Chitayat, Michael Kopeliovich, Yaacov Algebraic Topology Combinatorics 57N65, 05E14 Let $X$ be a compact Riemann surface of genus $g$ and let $x \in X$. We derive the classical presentation of $π_1(X,x)$ (i.e the one given by $2g$ generators $a_1,b_1, \dots, a_g,b_g$ and the relation $\prod_{i=1}^g[a_i,b_i] = 1$) from the description of $X$ as a branched cover $f : X \to \mathbb{C}\mathbb{P}^1$. |
| title | The Fundamental Group of a Compact Riemann Surface via Branched Covers |
| topic | Algebraic Topology Combinatorics 57N65, 05E14 |
| url | https://arxiv.org/abs/2501.18759 |