Consequences of the compatibility of skein algebra and cluster algebra on surfaces
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866910304922763264 |
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| author | Moon, Han-Bom Wong, Helen |
| author_facet | Moon, Han-Bom Wong, Helen |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_08833 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Consequences of the compatibility of skein algebra and cluster algebra on surfaces Moon, Han-Bom Wong, Helen Geometric Topology Commutative Algebra Algebraic Geometry 57K31, 13F60, 57K20 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. |
| title | Consequences of the compatibility of skein algebra and cluster algebra on surfaces |
| topic | Geometric Topology Commutative Algebra Algebraic Geometry 57K31, 13F60, 57K20 |
| url | https://arxiv.org/abs/2201.08833 |