2024/05/30 by Sike Wang, Wang, Sike, Helen Wong +1 · 2 citations
Computer Science · #57-08 #57K16 #57K31 #Cryptography and Residue Arithmetic #Distributed and Parallel Computing Systems #FOS: Mathematics #Geometric Topology (math.GT) #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2405.20159
openalex publication_date 2024/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.