QM Research Seminar: Sutured Legendrian stops and the conormal of braids.

Seminar by Côme Dattin (Uppsala University)

Abstract:

Starting with a Riemannian manifold M, its unit bundle UM is a contact manifold, whose Reeb vector field lifts the geodesic flow. Given a submanifold N, its unit conormal is a Legendrian submanifold in UM. Thus this construction takes us from the smooth world to the contact world, and one may use Legendrian invariants to study smooth (sub)manifolds.
In this talk we will show that, if the unit conormals of two surface braids are Legendrian isotopic (relatively to their boundary), then the braids are equivalent. The main tool will be an invariant of Legendrians with boundary, called the stopped sutured homology. Using its associated exact sequence, we recover a classical invariant of braids, namely an automorphism of the punctured surface.