Weak and strong fillability of higher dimensional contact manifolds

• 成果类型: Article
• 署名作者: Massot, Patrick; Niederkrueger, Klaus; Wendl, Chris
• 署名单位: Universite Paris Saclay; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; University of London; University College London
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-012-0412-5
• 发表日期: 2013
• 页码: 287-373
• 关键词: homology; CURVES

摘要

For contact manifolds in dimension three, the notions of weak and strong symplectic fillability and tightness are all known to be inequivalent. We extend these facts to higher dimensions: in particular, we define a natural generalization of weak fillings and prove that it is indeed weaker (at least in dimension five), while also being obstructed by all known manifestations of overtwistedness. We also find the first examples of contact manifolds in all dimensions that are not symplectically fillable but also cannot be called overtwisted in any reasonable sense. These depend on a higher dimensional analogue of Giroux torsion, which we define via the existence in all dimensions of exact symplectic manifolds with disconnected contact boundary.