Three-page indices of torus links
Abstract
An arc presentation of a link is an embedding into the open book decomposition of R3 with a finite number of pages. An important rule of arc presentations is that different arcs must be placed on separate pages. In 1999, Dynnikov proposed a three-page presentation that bends this rule by restricting the total number of pages to three. Dynnikov showed that every link admits a three-page presentation. In this paper, we provide an alternative proof of this result. Also we define the three-page index α3(L) of a link L that the minimum number of arcs needed to represent L in a three-page presentation. We examine three-page presentations for torus links, leading to the determination of the exact three-page indices for several torus links.
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