Symplectic fillings and spinal open books

The classification of the symplectic fillings of a given contact 3-manifold poses an interesting problem. It is motivated by results that demonstrate that the symplectic fillings of a contact 3-manifold hold information on the contact structure. Most notably, the contact structure of any contact 3-manifold that admits a strong symplectic filling is tight. Although the symplectic fillings of certain contact manifolds have been classified, the general classification remains an open problem. Working towards this, one can consider the geography problem for symplectic fillings. In the paper Spine removal surgery and the geography of symplectic fillings, Sam Lisi and Chris Wendl prove the existence of a universal bound for the geography (Euler characteristic and signature) of possible minimal strong symplectic fillings of a closed contact 3-manifold with a supporting planar spinal open book decomposition. Following a brief introduction to symplectic and contact topology, the aim of my talk is to explain Lisi and Wendl's result. For this purpose, I will provide an overview of symplectic fillings and the related geography problem, and introduce spinal open book decompositions.