Crowell's derived group and twisted polynomials

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The derived group of a permutation representation, introduced by R.H. Crowell, unites many notions of knot theory. We survey Crowell's construction, and offer new applications. The twisted Alexander group of a knot is defined. Using it, we obtain twisted Alexander modules and polynomials. Also, we extend a well-known theorem of Neuwirth and Stallings giving necessary and sufficient conditions for a knot to be fibered. Virtual Alexander polynomials provide obstructions for a virtual knot that must vanish if the knot has a diagram with an Alexander numbering. The extended group of a virtual knot is defined, and using it a more sensitive obstruction is obtained.
16 pages, 6 figures. Version 3 contains new material and extended exposition

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Geometric Topology, 57M25; Secondary 20F05, 20F34

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http://salesiana.dossiersoluciones.com/handle/123456789/102051

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0506339
 http://arxiv.org/abs/math/0506339

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arXiv