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

Michel Boileau; Yi Ni; Shicheng Wang

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arXiv · 0801.1943

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

Michel Boileau·Yi Ni·Shicheng Wang

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Abstract

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.

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BibTeX RIS

Michel Boileau, Yi Ni, Shicheng Wang. 2008-01-13. On standard forms of 1--dominations between knots with same Gromov volumes. https://arxiv.org/abs/0801.1943

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