Transverse knots and their branched covers

Olga Plamenevskaya, SUNY Stony Brook

A transverse knot in a contact manifold is a knot that is everywhere
transverse to contact planes.  A simple invariant called self-linking
number distinguishes different transverse knots that are smoothly
isotopic.  However, there exist different transverse knots of the same
smooth type and self linking number (many examples were given by
Birman--Menasco, Etnyre--Honda, and later by Ng--Ozsvath--Thurston).

In this talk, we discuss studying transverse knots via their cyclic
branched covers, which are contact manifolds naturally associated to
transverse knots. We show that in many cases branched covers of two
transverse knots are contactomorphic if the knots have the same smooth
type and self-linking number. (This is joint work with S.Harvey and
K.Kawamuro.)