Wrapped sutured Legendrian homology and the conormal of braids

In this talk we will discuss invariants of sutured Legendrians. A sutured contact manifold can be seen as either generalizing the contactisation of a Liouville domain, or as a presentation of a contact manifold with convex boundary. Using the first point of view, we define the wrapped sutured homology of Legendrians with boundary, employing ideas coming from Floer theory. To illustrate the second aspect, we apply the unit conormal construction to braids with two strands, which yields a sutured Legendrian. We will show that, if the conormals of two 2-braids are Legendrian isotopic, then the braids are equivalent.