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On fillability of contact manifolds
<span class="artikel autor" lang="de"> Klaus Niederkrüger </span>
http://tel.archives-ouvertes.fr/tel-00922320
Habilitation à diriger des recherches, Toulouse 2013
2013
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The aim of this text is to give an accessible overview to some recent results
concerning contact manifolds and their symplectic fillings. In particular, we work out the
weakest compatibility conditions between a symplectic manifold and a contact structure on
its boundary to still be able to obtain a sensible theory (Chapter II), furthermore we prove
two results (Theorem A and B in Section I.4) that show how certain submanifolds inside a
contact manifold obstruct the existence of a symplectic filling or influence its topology. We
conclude by giving several constructions of contact manifolds that for different reasons do not
admit a symplectic filling.