Séance Séminaire

Séminaire Algèbre Géométrie Algébrique Topologie Algébrique

Heegaard splittings and the tight Giroux Correspondence

An open book is a decomposition of a closed, oriented 3-manifold as the union of a link and a surface bundle over the circle. Although a topological object, an open book encodes additional geometric data on the manifold: a plane field called a contact structure. The relationship between open books encoding the same contact structure is described by a celebrated theorem known as the Giroux Correspondence. In the first part of the talk, I’ll introduce the objects and explain the statement of the Giroux Correspondence. In the second half of the talk, I’ll explain how the relationship between Heegaard splittings and open books leads to a new proof of an important case of the Giroux Correspondence; this result is joint work with V Vertesi.