On standard forms of 1--dominations between knots with same Gromov volumes

dc.creatorBoileau, Michel
dc.creatorNi, Yi
dc.creatorWang, Shicheng
dc.date2008-01-13
dc.date.accessioned2026-07-07T08:54:14Z
dc.date.available2026-07-07T08:54:14Z
dc.descriptionLet $k$ 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.description15 pages
dc.identifierhttps://arxiv.org/abs/0801.1943
dc.identifierhttp://arxiv.org/abs/0801.1943
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/145858
dc.subjectGeometric Topology
dc.subject57M25, 57M50, 55M20
dc.titleOn standard forms of 1--dominations between knots with same Gromov volumes
dc.typetext

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