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Skein relations for punctured surfaces

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arxiv 2409.04957 v2 pith:KMI4GLSH submitted 2024-09-08 math.CO

Skein relations for punctured surfaces

Esther Banaian , Wonwoo Kang , Elizabeth Kelley This is my paper
classification math.CO
keywords surfacespuncturedrelationsalgebrasclusterformskeinwork
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We investigate skein relations in cluster algebras from punctured surfaces, extending the work of \c{C}anak\c{c}i-Schiffler and Musiker-Williams on unpunctured surfaces. Using a combinatorial expansion formula by O{\u{g}}uz-Y{\i}ld{\i}r{\i}m 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.

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Cited by 4 Pith papers

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