Skein relations for punctured surfaces
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909396062175232 |
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| author | Banaian, Esther Kang, Wonwoo Kelley, Elizabeth |
| author_facet | Banaian, Esther Kang, Wonwoo Kelley, Elizabeth |
| contents | We investigate skein relations in cluster algebras from punctured surfaces, extending the work of Çanakçi-Schiffler and Musiker-Williams on unpunctured surfaces. Using a combinatorial expansion formula by O{ğ}uz-Yıldırım and Pilaud-Reading-Schroll, we provide explicit formulas for these relations. This work demonstrates that the punctured analogues of the bangle and bracelet functions form spanning sets for cluster algebras associated with a punctured surfaces. For surfaces with boundary and closed surfaces of genus 0, we further show that the bangles and bracelets form bases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_04957 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Skein relations for punctured surfaces Banaian, Esther Kang, Wonwoo Kelley, Elizabeth Combinatorics 13F60, 05E15, 06A06 We investigate skein relations in cluster algebras from punctured surfaces, extending the work of Çanakçi-Schiffler and Musiker-Williams on unpunctured surfaces. Using a combinatorial expansion formula by O{ğ}uz-Yıldırım and Pilaud-Reading-Schroll, we provide explicit formulas for these relations. This work demonstrates that the punctured analogues of the bangle and bracelet functions form spanning sets for cluster algebras associated with a punctured surfaces. For surfaces with boundary and closed surfaces of genus 0, we further show that the bangles and bracelets form bases. |
| title | Skein relations for punctured surfaces |
| topic | Combinatorics 13F60, 05E15, 06A06 |
| url | https://arxiv.org/abs/2409.04957 |