Topological notions for Kauffman and Vogel's polynomial
| dc.creator | Carpentier, Rui Pedro | |
| dc.date | 2002-04-16 | |
| dc.date.accessioned | 2026-07-07T04:47:44Z | |
| dc.date.available | 2026-07-07T04:47:44Z | |
| dc.description | In [2] Kauffman and Vogel constructed a rigid vertex regular isotopy invariant for unoriented four-valent graphs embedded in three dimensional space. It assigns to each embedded graph G a polynomial, denoted [G], in three variables, A, B and a, satisfying three skein relations, and is defined in terms of a state-sum and the Dubrovnik polynomial for links. In previous work by the author it is proved, in the case B=A^{-1} and a=A, that for a planar graph G we have [G]=2^{c-1}(-A-A^{-1})^v, where c is the number of connected components of G and v is the number of vertices of G. In this paper we will show how we can calculate the polynomial for embedded graphs, with the variables B=A^{-1} and a=A, without resorting to the skein relation. | |
| dc.description | 12 pages, 5 figures and many eps files for the skein relations. To appear in J. Knot Theory Ramifications | |
| dc.identifier | https://arxiv.org/abs/math/0204207 | |
| dc.identifier | http://arxiv.org/abs/math/0204207 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63835 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M15; 05C10; 57M27 | |
| dc.title | Topological notions for Kauffman and Vogel's polynomial | |
| dc.type | text |