Band description of knots and Vassiliev invariants
| dc.creator | Taniyama, Kouki | |
| dc.creator | Yasuhara, Akira | |
| dc.date | 2000-03-03 | |
| dc.date.accessioned | 2026-07-07T04:34:11Z | |
| dc.date.available | 2026-07-07T04:34:11Z | |
| dc.description | In 1993 K. Habiro defined $C_k$-move of oriented links and around 1994 he proved that two oriented knots are transformed into each other by $C_k$-moves if and only if they have the same Vassiliev invariants of order $\leq k-1$. In this paper we define Vassiliev invariant of type $(k_1,...,k_l)$, and show that, for $k=k_1+...+k_l$, two oriented knots are transformed into each other by $C_k$-moves if and only if they have the same Vassiliev invariants of type $(k_1,...,k_l)$. We introduce a concept ` band description of knots' and give a diagram-oriented proof of this theorem. When $k_1=...=k_l=1$, the Vassiliev invariant of type $(k_1,...,k_l)$ coincides with the Vassiliev invariant of order $\leq l-1$ in the usual sense. As a special case, we have Habiro's theorem stated above. | |
| dc.description | LaTeX, 16 pages with 22 figures | |
| dc.identifier | https://arxiv.org/abs/math/0003021 | |
| dc.identifier | http://arxiv.org/abs/math/0003021 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/58805 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M25 | |
| dc.title | Band description of knots and Vassiliev invariants | |
| dc.type | text |