Georgia Institute of Technology College of Sciences

Knots in contact manifolds are interesting objects to study. In this talk, I will focus on knots in overtwisted manifolds. There are two types of knots in an overtwisted manifold, one with overtwisted complement (known as loose) and one with tight complement (known as non-loose). Not very surprisingly, non-loose knots behave very mysteriously. They are interesting in their own right as we still do not understand them well. But also one might want to study them because surgery on them produces tight contact structures and understanding tight contact structures is a major problem in the contact world. I'll give a brief history on these knots and discuss some of their classification and structure problems and how these problems differ from the classification/ structure problems of knots in tight manifolds.