Cable links of uniformly thick knot types

Abstract: In this paper, we study Legendrian realizations of cable links of knot types that are uniformly thick but not Legendrian simple, extending prior work of Dalton, the second author, and Traynor. This leads to new phenomena, such as Legendrian links that are smoothly isotopic and component-wise Legendrian isotopic, but are not Legendrian isotopic. In our study, we establish new results for cable links whose cable slope is sufficiently negative. We will also show how to classify Legendrian knots in (most) negative cables of twist knots. This is done by introducing a new technique to the study of cables based on Legendrian surgeries.