Spinal Open Book Decompositions

Speaker: Sam Lisi, University of Mississippi.

Date: 25 nov 2019, 14h.

Place: Room 201, Bloco H, Campus Gragoatá, UFF.

Abstract: Contact manifolds admit many different descriptions, and examples can be constructed from many points of view. One natural class comes as the boundary "at infinity" of a (non-compact) symplectic manifold with a homogeneity condition -- the prototypical example is seeing the unit co-tangent bundle as the boundary of T*Q. Another description comes from an open book decomposition.

The symplectic filling problem for a contact manifold is, given a contact manifold, to determine if it arises as the boundary of a symplectic manifold, and if so, to classify all the symplectic fillings.

To address this question, at least in some cases, we introduce the notion of a spinal open book decomposition in dimension 3. Using J-holomorphic curve techniques, we obtain filling obstructions for a class of examples (using ideas originally developed by Gromov, McDuff and Eliashberg) and a complete filling classification for a smaller class of examples (using ideas from Hofer-Wysocki-Zehnder, Hutchings and Siefring).  I will give some examples of what we are able to classify, and will also illustrate some of the less technical ingredients of the proofs.

This is joint work with Jeremy Van Horn-Morris and Chris Wendl.