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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.20159 |
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Table of Contents:
- The Kauffman bracket skein algebra of a surface is a generalization of the Jones polynomial invariant for links and plays a principal role in the Witten-Reshetikhin- Turaev topological quantum field theory. However, the multiplicative structure of the skein algebra is not well understood, with a priori exponential complexity. We consider the case of one-hole torus, and provide a polynomial algorithm for computing multiplication of any two skein elements. Some closed form formulas for multiplication of curves with low crossing number are also given.