An algorithm for comparing Legendrian links

Geometry Topology Seminar
Wednesday, October 18, 2023 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 006
Ivan Dynnikov – Steklov Mathematical Institute –
Thang Le

The talk is based on my joint works with Maxim Prasolov and Vladimir Shastin, where we studied the relation between rectangular diagrams of links and Legendrian links. This relation allows for a complete classification of exchange classes of rectangular diagrams in terms of equivalence classes of Legendrian links and their symmetry groups. Since all rectangular diagrams of given complexity can be searched, this yields a method to algorithmically compare Legendrian links. Of course, the general algorithm has too high complexity for a practical implementation, but in some situations, the most time consuming parts can be bypassed, which allows us to confirm the non-equivalence of Legendrian knots in several previously unresolved cases.