On knots in overtwisted contact structures
Journal of Quantum Topology 4 (2013), 229--264.

We prove that each overtwisted contact structure has knot types that are represented by infinitely many distinct transverse knots all with the same self-linking number. In some cases, we can even classify all such knots. We also show similar results for Legendrian knots and prove a ``folk'' result concerning loose transverse and Legendrian knots (that is knots with overtwisted complements) which says that such knots are determined by their classical invariants (up to contactomorphism). Finally we discuss how these results partially fill in our understanding of the ``geography" and ``botany'' problems for Legendrian knots in overtwisted contact structures, as well as many open questions regarding these problems.

You may download a pdf version of this paper.

You may download the published version of this paper. (Access may be restricted.)

You may download the version of this paper at the arxiv.

This paper has been reviewd in math reviews. (Access may be restricted.)

Return to my home page.