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On multiplying curves in the Kauffman bracket skein algebra of the thickened four-holed sphere.
- Source :
-
Journal of Knot Theory & Its Ramifications . Dec2021, Vol. 30 Issue 14, p1-29. 29p. - Publication Year :
- 2021
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *ALGEBRA
*TORUS
*LOGICAL prediction
*ALGORITHMS
Subjects
Details
- Language :
- English
- ISSN :
- 02182165
- Volume :
- 30
- Issue :
- 14
- Database :
- Academic Search Index
- Journal :
- Journal of Knot Theory & Its Ramifications
- Publication Type :
- Academic Journal
- Accession number :
- 156279478
- Full Text :
- https://doi.org/10.1142/S0218216521410017