Monotonic simplification of rectangular diagrams and contact topology

Geometry Topology Seminar
Monday, March 25, 2013 - 14:00
1 hour (actually 50 minutes)
Skiles 006
Moscow State University
A few years ago I proved that any rectangular diagram of the unknot admits monotonic simplification by elementary moves. More recently M.Prasolov and I addressed the question: when a rectangular diagram of a link admits at least one step of simplification? It turned out that an answer can be given naturally in terms of Legendrian links. On this way, we resolved positively a conjecture by V.Jones on the invariance of the algebraic crossing number of a minimal braid, and a few similar questions.