subcrit Subcritical contact surgeries and the topology of symplectic fillings Paolo Ghiggini Klaus Niederkrüger Chris Wendl http://arxiv.org/abs/1408.1051 arXiv 1408.1051 2014 none.jpg By a result of Eliashberg, every symplectic filling of a three-dimensional contact connected sum is obtained by performing a boundary connected sum on another symplectic filling. We prove a partial generalization of this result for subcritical contact surgeries in higher dimensions: given any contact manifold that arises from another contact manifold by subcritical surgery, its belt sphere must be nullhomologous in any semipositive filling, and in dimension five, it must be nullhomotopic in any symplectically aspherical filling. The proof is based on disk-filling techniques with families of Legendrian open books (so-called "LOBs") as boundary conditions. We also illustrate the method by giving a new proof of the Eliashberg-Floer-McDuff theorem on symplectic fillings of spheres, which may be seen as a special case of our main result.