Cusp volumes of alternating knots
In the paper under review, the authors show that the area of the boundary of the maximal cusp for a hyperbolic alternating knot can be bounded above and below by a linear function of the twist number of an alternating diagram of the knot. NEWLINENEWLINEAs a corollary, diagrammatic estimates on Euclidean lengths of slopes for such knots are given. This implies that, for any closed 3-manifold with sufficiently large Gromov norm, there are at most finitely many prime alternating knots such that the manifold is obtained by Dehn surgery along the knot. Also it is implied that there is a universal lower bound on the cusp density of hyperbolic alternating knots.
scientific article; zbMATH DE number 6628600