Hyperbolic semi-adequate links (Q265095)

A Kauffman state for a link diagram is a resolution of every crossing in the diagram. Given a state, both a graph and a spanning surface for the link, called a state surface, can be constructed. A link is semi-adequate if a graph created by resolving all crossings of a diagram the same way has no single-edge loops. The class of semi-adequate links contains other well-studied classes, such as alternating and positive links.NEWLINENEWLINEThe main result of this paper is a criterion to show that a semi-adequate link is hyperbolic. The criterion can readily be checked for any semi-adequate diagram. Using this the authors demonstrate the hyperbolicity of classes of links, some of which were known by previous theorems and some of which were not. Links satisfying this criterion are further studied by \textit{A. Giambrone} [J. Knot Theory Ramifications 24, No. 1, Article ID 1550001, 21 p. (2015; Zbl 1332.57009)].NEWLINENEWLINEThe paper builds on machinery developed previously by the authors [Guts of surfaces and the colored Jones polynomial. Berlin: Springer (2013; Zbl 1270.57002)]. It is used to identify essential tori and annuli within the link complement by considering intersections with the state surface. Based on this exploration of tori, the authors also conjecture that if a semi-adequate link is a satellite link then this is visible in the semi-adequate diagram.