Knots in overtwisted contact manifolds

Rima Chaterjee (University of Cologne)

Knots associated to overtwisted manifolds are less explored. There are two types of knots in an overtwisted manifold – loose and non-loose. Non-loose knots are knots with tight complements where as
loose knots have overtwisted complements. While we understand loose knots, non-loose knots remain a mystery. The classification and structure problems of these knots vary greatly compared to the knots
in tight manifolds. In this talk, I’ll give a brief survey followed by some interesting recent work. Especially I’ll show how satellite operations on a knot in overtwisted manifold changes the geometric
property of the knot. I will discuss under what conditions cabling operation on a non-loose knot preserves non-looseness. The ”recent part” of this talk is based on joint work  with Etnyre, Min and Mukherjee.