3-Manifold Seminar: What is an alternating knot?

Seminar | November 27 | 2:10-3:30 p.m. | 939 Evans Hall

 Kyle Miller, UC BERKELEY

 Department of Mathematics

An alternating link is a link with a diagram having alternating over- and under-crossings as one traverses each component. Such links have interesting properties, for example the Tait conjectures and the existence of hyperbolic volume of non-torus alternating link complements. A question attributed to Ralph Fox is whether alternating knots have an intrinsic non-diagrammatic characterization. In November 2015, Josh Greene and Josh Howie each independently answered this question in terms of the existence of a pair of spanning surfaces with certain properties that are already satisfied by the alternating diagram's checkerboard surfaces. We will discuss these papers.