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Habilitation À Diriger Des Recherches Year : 2013

On fillability of contact manifolds

Abstract

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.
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Dates and versions

tel-00922320 , version 1 (25-12-2013)

Identifiers

  • HAL Id : tel-00922320 , version 1

Cite

Klaus Niederkrüger. On fillability of contact manifolds. Differential Geometry [math.DG]. Université Paul Sabatier - Toulouse III, 2013. ⟨tel-00922320⟩
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