# An alternative basis for the Kauffman bracket skein module of the Solid Torus via braids

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## Abstract

In this paper we give an alternative basis, $$\mathscr {b}_\mathrm{st}$$, for the kauffman bracket skein module of the solid torus, $$\mathrm{kbsm}\left( \mathrm{st}\right)$$. The basis $$\mathscr {b}_\mathrm{st}$$ is obtained with the use of the tempereley–lieb algebra of type b and it is appropriate for computing the kauffman bracket skein module of the lens spaces l(p, q) via braids.keywordskauffman bracket polynomialskein modulessolid torustemperley–lieb algebra of type bmixed linksmixed braidslens spaces2010 mathematics subject classification57m2757m2520f3620f3820c08.
Original language English Knots, Low-Dimensional Topology and Applications (KNOTS16) Knots in Hellas, International Olympic Academy, Greece, July 2016 Colin C. Adams, Cameron McA. Gordon, Vaughan F.R. Jones, Louis H. Kauffman, Sofia Lambropoulou, Kenneth C. Millett, Jozef H. Przytycki, Renzo Ricca, Radmila Sazdanovic Springer, Cham 329-345 978-3-030-16031-9 978-3-030-16030-2 https://doi.org/10.1007/978-3-030-16031-9_16 Published - 2019 Yes

### Publication series

Series Springer Proceedings in Mathematics and Statistics 284 2194-1009