For an un-oriented link $\mathcal{ K}$, let $L(\mathcal{ K})$ be the ropelength of $\mathcal{ K}$. It is known that when $\mathcal{ K}$ has more than one component, different orientations of the components of $\mathcal{ K}$ may result in different braid index. We define the largest braid index among all braid indices corresponding to all possible orientation assignments of $\mathcal{ K}$ the { \em absolute braid index} of $\mathcal{ K}$ and denote it by $\textbf{ B}(\mathcal{ K})$. In this paper, we show that there exists a constant $a>0$ such that $L(\mathcal{ K})\ge a \textbf{ B}(\mathcal{ K}) $ for any $\mathcal{ K}$, { \em i.e.}, the ropelength of any link is bounded below by its absolute braid index (up to a constant factor).
Categories: math.GT