Slope lengths and generalized augmented links
Abstract
Description
In this paper, we determine geometric information on slope lengths of a large class of knots in the 3-sphere, based only on diagrammatical properties of the knots. In particular, we show such knots have meridian length strictly less than 4, and we find infinitely many families with meridian length approaching 4 from below. Finally, we present an example to show that, in contrast to the case of the regular augmented link, longitude lengths of these knots cannot be determined by a function of the number of twist regions alone.
v2: 20 pages, 13 figures. Simplified proofs of main results and added two sections, one giving examples of knots with meridian lengths approaching the upper bound of 4, and one showing that there are no bounds on longitude length in terms of twist number. Updated the title to reflect these changes. To appear Comm. Anal. Geom
v2: 20 pages, 13 figures. Simplified proofs of main results and added two sections, one giving examples of knots with meridian lengths approaching the upper bound of 4, and one showing that there are no bounds on longitude length in terms of twist number. Updated the title to reflect these changes. To appear Comm. Anal. Geom