Isotopy classes of crossing arcs in hyperbolic alternating links
Location: Hill 525
Date & time: Tuesday, 11 October 2016 at 3:30PM - 3:31PM
Anastasiia Tsvietkova, Rutgers University, Newark: For hyperbolic alternating links, it has been suspected for many years that every arc in the reduced alternating diagram running from an overcrossing to an undercrossing is isotopic to a geodesic. This was conjectured by Sakuma and Weeks in 1995. Since then, it has been proved only for several families of links. We obtain conditions that guarantee that a link complement has a complete hyperbolic structure (without using Geometrization), and every such arc is isotopic to a simple geodesic. Our conditions also ensure that crossing arcs are the edges of an ideal geodesic triangulation. We provide new infinite families of links for which this holds.