Topology seminar

I will talk about our recent work with Maxim Prasolov in which we unexpectedly proved Jones' conjecture which states that the algebraic crossing number of a braid whose closure is the given link is an invariant of the link provided that the braid index is minimal. This work started from discovering a criteria when a rectangular diagram of a link admits a destabilization after applying finitely many elementary moves preserving the number of edges.

It turns out that the two Legendrian links naturally associated to each rectangular diagram are responsible for this property.