  A transverse knot is a knot that is transverse to the planes of the standard
contact structure on real 3-space. In this paper we prove the Markov Theorem
for transverse braids, which states that two transverse closed braids that are
isotopic as transverse knots are also isotopic as transverse braids. The
methods of the proof are based on Birman and Menasco's proof of the Markov
Theorem in their recent paper (BM02), modified to the transverse setting. The
modification is straightforward until we get to the special case of preferred
longitudes, where we need some new machinery. We use techniques from earlier
work by the author with Birman (BW00), by Birman and Menasco ((BM4), for
example), and develop new methods from Cromwell's paper on arc-presentations
(Cr95).
