Back to Cascade Fall 2007
Back to Schedule

---

Oliver Dasbach
The Jones polynomial and graphs on surfaces

Turaev constructed to each knot diagram an orientable surface on which the knot projects alternatingly. The induced checkerboard graphs are thus two graphs embedded on the Turaev surface that are dual to each other. We show that the Bollobas-Riordan-Tutte polynomial of either of these checkerboard graphs specialices to the Jones polynomial of the knot. We will give some applications of this approach.