Appears in collection : 2021 - T2 - WS2 - Advances in symplectic topology

Let S be a convex hypersurface with neighborhood N(S) inside of some contact manifold. When dim(S)=2 the contact topology of N(S) is governed by simple closed curves on S. However, few tools are currently available to study N(S) when dim(S)>2. We provide such a tool which is applicable in any dimension by computing the sutured contact homology of N(S) in terms of linearized invariants of the positive and negative regions of S. The proof combines Morse-Bott, obstruction bundle gluing, and virtual perturbation techniques.