Torsion in Kauffman bracket skein module of a $4$-strand Montesinos knot exterior
| Autor: | Chen, Haimiao |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | For an oriented $3$-manifold $M$, let $\mathcal{S}(M)$ denote its Kauffman bracket skein module over $\mathbb{Z}[q^{\pm\frac{1}{2}}]$. It is shown that $\mathcal{S}(M)$ admits infinitely many torsion elements when $M$ is the exterior of the Montesinos knot $K(a_1/b_1,a_2/b_2,a_3/b_4,a_4/b_4)\subset S^3$ with each $b_i\ge 3$. This provides a negative answer to Problem 1.92 (G)-(i) in the Kirby's list, which asks whether $\mathcal{S}(M)$ is free when $M$ is irreducible and has no incompressible non-boundary parallel torus. Comment: 22 pages, 21 figures. Some errors are fixed and the writing is further improved. This edition is very readable. Comments are welcome! |
| Databáze: | arXiv |
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