Crowell's derived group and twisted polynomials
| dc.creator | Silver, Daniel S. | |
| dc.creator | Williams, Susan G. | |
| dc.date | 2005-06-16 | |
| dc.date | 2006-08-04 | |
| dc.date.accessioned | 2026-07-07T06:42:28Z | |
| dc.date.available | 2026-07-07T06:42:28Z | |
| dc.description | 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. | |
| dc.description | 16 pages, 6 figures. Version 3 contains new material and extended exposition | |
| dc.identifier | https://arxiv.org/abs/math/0506339 | |
| dc.identifier | http://arxiv.org/abs/math/0506339 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/102051 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M25; Secondary 20F05, 20F34 | |
| dc.title | Crowell's derived group and twisted polynomials | |
| dc.type | text |