Consequences of the compatibility of skein algebra and cluster algebra on surfaces

Han-Bom Moon; Helen Wong

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arXiv · 2201.08833

Consequences of the compatibility of skein algebra and cluster algebra on surfaces

Han-Bom Moon·Helen Wong

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Abstract

We investigate two algebra of curves on a topological surface with punctures - the cluster algebra of surfaces defined by Fomin, Shapiro, and Thurston, and the generalized skein algebra constructed by Roger and Yang. By establishing their compatibility, we resolve Roger-Yang's conjecture on the deformation quantization of the decorated Teichmuller space. We also obtain several structural results on the cluster algebra of surfaces. The cluster algebra of a positive genus surface is not finitely generated, and it differs from its upper cluster algebra.

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Han-Bom Moon, Helen Wong. 2022-01-21. Consequences of the compatibility of skein algebra and cluster algebra on surfaces. https://arxiv.org/abs/2201.08833

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