论文标题
交替结的隆起猜想
The ropelength conjecture of alternating knots
论文作者
论文摘要
长期存在的猜想指出，任何交替结的ropeenthent至少与其交叉数量成正比。在本文中，我们证明了这个猜想是正确的。也就是说，存在一个常数$ b_0> 0 $，因此任何交替结$ k $的$ r（k）\ ge b_0cr（k）$，其中$ r（k）$是$ k $的ropelength，$ k $和$ cr（k）$是$ k $的交叉数。在本文中，我们证明了这个猜想是正确的。
A long standing conjecture states that the ropelength of any alternating knot is at least proportional to its crossing number. In this paper we prove that this conjecture is true. That is, there exists a constant $b_0>0$ such that $R(K)\ge b_0Cr(K)$ for any alternating knot $K$, where $R(K)$ is the ropelength of $K$ and $Cr(K)$ is the crossing number of $K$. In this paper, we prove that this conjecture is true.
