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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2307.11376 |
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| _version_ | 1866909845013135360 |
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| author | Geiß, Christof Labardini-Fragoso, Daniel |
| author_facet | Geiß, Christof Labardini-Fragoso, Daniel |
| contents | Let $(Σ,\mathbb{M},\mathbb{P})$ be a surface with marked points $\mathbb{M}\subseteq \partialΣ\neq\varnothing$ and punctures $\mathbb{P}\subseteqΣ\setminus\partialΣ$. In this paper we show that for every curve $γ$ on $Σ\setminus\mathbb{P}$, the curve obtained by resolving the kinks of $γ$ in any order is uniquely determined, up to homotopy in $Σ\setminus\mathbb{P}$, by the $2$-orbifold homotopy class of $γ$, in which the punctures are interpreted to be orbifold points of order $2$. Our proof resorts to an application of the Diamond Lemma. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_11376 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the resolution of kinks of curves on punctured surfaces Geiß, Christof Labardini-Fragoso, Daniel Geometric Topology Combinatorics Representation Theory 57K20, 13F60, 18B40 Let $(Σ,\mathbb{M},\mathbb{P})$ be a surface with marked points $\mathbb{M}\subseteq \partialΣ\neq\varnothing$ and punctures $\mathbb{P}\subseteqΣ\setminus\partialΣ$. In this paper we show that for every curve $γ$ on $Σ\setminus\mathbb{P}$, the curve obtained by resolving the kinks of $γ$ in any order is uniquely determined, up to homotopy in $Σ\setminus\mathbb{P}$, by the $2$-orbifold homotopy class of $γ$, in which the punctures are interpreted to be orbifold points of order $2$. Our proof resorts to an application of the Diamond Lemma. |
| title | On the resolution of kinks of curves on punctured surfaces |
| topic | Geometric Topology Combinatorics Representation Theory 57K20, 13F60, 18B40 |
| url | https://arxiv.org/abs/2307.11376 |