On the Genus of One Degree of Freedom Planar Linkages via Tropical Geometry
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915127481073664 |
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| author | Schicho, Josef Tewari, Ayush Kumar Warren, Audie |
| author_facet | Schicho, Josef Tewari, Ayush Kumar Warren, Audie |
| contents | This paper focuses on studying the configuration spaces of graphs realised in $\mathbb C^2$, such that the configuration space is, after normalisation, one dimensional. If this is the case, then the configuration space is, generically, a smooth complex curve, and can be seen as a Riemann surface. The property of interest in this paper is the genus of this curve. Using tropical geometry, we give an algorithm to compute this genus. We provide an implementation in Python and give various examples. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_00449 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Genus of One Degree of Freedom Planar Linkages via Tropical Geometry Schicho, Josef Tewari, Ayush Kumar Warren, Audie Metric Geometry Combinatorics 52C25, 70B15, 14T90 This paper focuses on studying the configuration spaces of graphs realised in $\mathbb C^2$, such that the configuration space is, after normalisation, one dimensional. If this is the case, then the configuration space is, generically, a smooth complex curve, and can be seen as a Riemann surface. The property of interest in this paper is the genus of this curve. Using tropical geometry, we give an algorithm to compute this genus. We provide an implementation in Python and give various examples. |
| title | On the Genus of One Degree of Freedom Planar Linkages via Tropical Geometry |
| topic | Metric Geometry Combinatorics 52C25, 70B15, 14T90 |
| url | https://arxiv.org/abs/2408.00449 |