On standard forms of 1--dominations between knots with same Gromov volumes
| dc.creator | Boileau, Michel | |
| dc.creator | Ni, Yi | |
| dc.creator | Wang, Shicheng | |
| dc.date | 2008-01-13 | |
| dc.date.accessioned | 2026-07-07T08:54:14Z | |
| dc.date.available | 2026-07-07T08:54:14Z | |
| dc.description | Let $k$ and $k'$ be two knots in 3-sphere. Say $k$ 1--dominates $k'$, if there is a proper degree 1 map $f\co E(k)\to E(k')$, between knot exterior of $k_i$. Theorem: Suppose that any companion of $k$ is prime. If $k$ 1--dominates $k'$ with the same Gromov volume, then $k'$ can be obtained from $k$ by finitely many de-satellizations. The condition of "same Gromov volume" clearly can not be removed. We also give a new construction of 1-domination between knots with same Gromov volume to show that the condition "any companion of $k$ is prime" can not be removed. | |
| dc.description | 15 pages | |
| dc.identifier | https://arxiv.org/abs/0801.1943 | |
| dc.identifier | http://arxiv.org/abs/0801.1943 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/145858 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M25, 57M50, 55M20 | |
| dc.title | On standard forms of 1--dominations between knots with same Gromov volumes | |
| dc.type | text |