Construction of non-loose knots via cabling

Abstract: Knots in contact manifolds are interesting objects to study. In this talk, I’ll focus on knots in overtwisted manifolds with tight complements also known as non-loose knots. These knots play an important role in contact topology as one can get interesting tight contact manifolds by doing surgery on them, though they appear to be rare. I’ll briefly mention some of their existence results and then show that the cabling construction of these knots will give us a family of non-loose knots but only under certain conditions. This is joint work with Etnyre, Min and Mukherjee.