Slope lengths and generalized augmented links

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.

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Published 1 January 2008