Local moves on spatial graphs and finite type invariants
| dc.creator | Taniyama, Kouki | |
| dc.creator | Yasuhara, Akira | |
| dc.date | 2001-06-20 | |
| dc.date.accessioned | 2026-07-07T04:42:15Z | |
| dc.date.available | 2026-07-07T04:42:15Z | |
| dc.description | We define $A_k$-moves for embeddings of a finite graph into the 3-sphere for each natural number $k$. Let $A_k$-equivalence denote an equivalence relation generated by $A_k$-moves and ambient isotopy. $A_k$-equivalence implies $A_{k-1}$-equivalence. Let ${\cal F}$ be an $A_{k-1}$-equivalence class of the embeddings of a finite graph into the 3-sphere. Let ${\cal G}$ be the quotient set of ${\cal F}$ under $A_k$-equivalence. We show that the set ${\cal G}$ forms an abelian group under a certain geometric operation. We define finite type invariants on ${\cal F}$ of order $(n;k)$. And we show that if any finite type invariant of order $(1;k)$ takes the same value on two elements of ${\cal F}$, then they are $A_k$-equivalent. $A_k$-move is a generalization of $C_k$-move defined by K. Habiro. Habiro showed that two oriented knots are the same up to $C_k$-move and ambient isotopy if and only if any Vassiliev invariant of order $\leq k-1$ takes the same value on them. The ` if' part does not hold for two-component links. Our result gives a sufficient condition for spatial graphs to be $C_k$-equivalent. | |
| dc.description | LaTeX, 18 pages with figures, to appear in Pacific Journal of Mathematics | |
| dc.identifier | https://arxiv.org/abs/math/0106173 | |
| dc.identifier | http://arxiv.org/abs/math/0106173 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61699 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M25 (Primary) 57M15 (Secondary) | |
| dc.title | Local moves on spatial graphs and finite type invariants | |
| dc.type | text |