Abstract
The aim of this notes is to explain some non-fillability results in higher dimensional contact topology, which are closely related to the question of how to define overtwistedness. We start with an overview of some basic examples and theorems known so far, comparing them with analogous results in dimension three. We will also describe an easy construction of non-fillable manifolds by Fran Presas. Then we will explain how to use holomorphic curves with boundary to prove the non-fillability results stated earlier. No a priori knowledge of holomorphic curves will be required; though many properties will only be quoted.
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Niederkrüger, K. (2014). Higher Dimensional Contact Topology via Holomorphic Disks. In: Bourgeois, F., Colin, V., Stipsicz, A. (eds) Contact and Symplectic Topology. Bolyai Society Mathematical Studies, vol 26. Springer, Cham. https://doi.org/10.1007/978-3-319-02036-5_5
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