具有相同Gromov体积的纽结之间1-支配的标准式
On standard forms of 1--dominations between knots with same Gromov volumes
摘要：
设$k$和$k'$是三维球面中的两个纽结。假设$k$ 1-支配$k'$，如果在$k_i$的节点外部之间存在适当的1度映射$f\co E(k)\to E(k')$。定理：设$k$的任一伴都是素数。如果$k$ 1--以相同的Gromov体积支配$k'$，则可以通过多次去卫星化从$k$获得$k'$。“相同的格罗莫夫体积”的条件显然不能被删除。我们还给出了具有相同Gromov体积的纽结之间的1-支配的一个新的构造，以证明“$k$的任何伴是素的”这一条件不能被去掉.
英文摘要：
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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