Côme Dattin: Wrapped sutured homology and the conormal of braids

Abstract: 

Starting with a submanifold (which might have boundary), its unit conormal is a Legendrian submanifold in the unit bundle of the ambient manifold. Thus, the unit conormal construction takes us from the smooth world to the contact world, and one may wonder which information is preserved. In this talk we will show that, if the conormals of two braids (with 2 strands, for a simple case) are Legendrian isotopic, then the braids are equivalent. The main tool will be the wrapped sutured homology, an invariant of Legendrians with boundary, with its associated exact sequence. If time permits, we will also sketch some ideas for the general situation.