RT Journal Article
T1 On multiplying curves in the Kauffman bracket skein algebra of the thickened four-holed sphere
A1 Bakshi, Rhea Palak
A1 Mukherjee, Sujoy
A1 Przytycki, Józef H.
A1 Silvero, Marithania
A1 Wang, Xiao
AB Based on the presentation of the Kauffman bracket skein algebra of the thickened torus given by the third author in previous work [4], Frohman and Gelca established a complete description of the multiplicative operation leading to a famous product-to-sum formula. In this paper, we study the multiplicative structure of the Kauffman bracket skein algebra of the thickened four-holed sphere. We present an algorithm to compute the product of any two elements of the algebra, and give an explicit formula for some families of curves. We surmise that the algorithm has quasi-polynomial growth with respect to the number of crossings of a pair of curves. Further, we conjecture the existence of a positive basis for the algebra.
PB World Scientific Publishing
SN 0218-2165
SN 1793-6527 (electrónico)
YR 2022
FD 2022
LK http://hdl.handle.net/10272/21247
UL http://hdl.handle.net/10272/21247
LA eng
NO Bakshi, R. P., Mukherjee, S., Przytycki, J. H., Silvero, M., & Wang, X. (2021). On multiplying curves in the Kauffman bracket skein algebra of the thickened four-holed sphere. In Journal of Knot Theory and Its Ramifications (Vol. 30, Issue 14). World Scientific Pub Co Pte Ltd. https://doi.org/10.1142/s0218216521410017
DS Repositorio Institucional de la Universidad de Huelva
RD 1 jun 2026