Vassiliev invariants and rational knots of unknotting number one
| dc.creator | Stoimenow, A. | |
| dc.date | 1999-09-09 | |
| dc.date | 2001-12-20 | |
| dc.date.accessioned | 2026-07-07T05:30:43Z | |
| dc.date.available | 2026-07-07T05:30:43Z | |
| dc.description | Introducing a way to modify knots using $n$-trivial rational tangles, we show that knots with given values of Vassiliev invariants of bounded degree can have arbitrary unknotting number (extending a recent result of Ohyama, Taniyama and Yamada). The same result is shown for 4-genera and finite reductions of the homology group of the double branched cover. Closer consideration is given to rational knots, where it is shown that the number of $n$-trivial rational knots of at most $k$ crossings is for any $n$ asymptotically at least $C^{(\ln k)^2}$ for any $C<\sqrt[2\ln 2]{e}$. | |
| dc.description | 13 pages, 2 figures; revision 26 Nov 99: added reference [OTY], discussion of signatures, branched cover homology and 4-genera, more problems; revision 7 Sep 01: Theorem 1.2 slightly improved, a few other minor structural changes; revision 20 Dec 01: final version, Theorem 1.2 improved, 2 sections removed | |
| dc.identifier | https://arxiv.org/abs/math/9909050 | |
| dc.identifier | http://arxiv.org/abs/math/9909050 | |
| dc.identifier | Topology 42(1) (2003), 227--241. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79080 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M25 | |
| dc.title | Vassiliev invariants and rational knots of unknotting number one | |
| dc.type | text |