Computing the Conway polynomial of several closures of oriented 3-braids
"This paper deals with polynomial invariants of a class of oriented 3-string tangles and the knots (or links) obtained by applying six different closures. In Cabrera-Ibarra (2004) [1], expressions were given to compute the Conway polynomials of four different closures of the composition of two...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2012 |
| País: | México |
| Institución: | Instituto Potosino de Investigación Científica y Tecnológica |
| Repositorio: | Repositorio Institucional del IPICYT |
| OAI Identifier: | oai:ipicyt.repositorioinstitucional.mx:1010/1493 |
| Acceso en línea: | http://ipicyt.repositorioinstitucional.mx/jspui/handle/1010/1493 |
| Access Level: | acceso abierto |
| Palabra clave: | info:eu-repo/classification/Autor/Conway polynomial info:eu-repo/classification/Autor/3-Tangle info:eu-repo/classification/Autor/3-BraidClosure info:eu-repo/classification/Autor/Continued fraction info:eu-repo/classification/cti/1 info:eu-repo/classification/cti/12 |
| Sumario: | "This paper deals with polynomial invariants of a class of oriented 3-string tangles and the knots (or links) obtained by applying six different closures. In Cabrera-Ibarra (2004) [1], expressions were given to compute the Conway polynomials of four different closures of the composition of two such 3-string tangles. By using the expressions and results from that reference, and using an algorithm developed on the basis of Gillerʼs calculations for 3-string tangles, we provide new results concerning six closures of 3-braids. Surprisingly, for 3-braids two of the closures turn out to be affine functions of the four previously defined. Among the contributions in this paper one finds computational tools to obtain the Conway polynomial of closures of 3-braids in terms of continuous fractions and their expansions. An interesting feature is that our calculations yield explicit, nonrecursive formulas in the case of 3-braids, thereby considerably lowering the time required to compute them. As a byproduct, explicit expressions are also given to obtain both numerators and denominators of continuous fractions in a nonrecursive way." |
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