Determining isotopy classes of crossing arcs in alternating links
arXiv:1411.0231
Abstract
Given a reduced alternating diagram for a link, we obtain conditions that guarantee that the link complement has a complete hyperbolic structure, crossing arcs are the edges of an ideal geodesic triangulation, and every crossing arc is isotopic to a simple geodesic. The latter was conjectured by Sakuma and Weeks in 1995. We provide infinite families of closed braids for which our conditions hold.
To appear in Asian Journal of Matematics. 18 pages, 12 figures