2018/10/31 by Bahar Acu, Agustin Moreno · 3 citations
Mathematics · #Generalization #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Iterated function #Planar #Planarity testing #Symplectic geometry #math.GT #math.SG #msc:32Q65 #msc:57R17
paper · pdf · doi:10.1093/imrn/rnaa155
published in International Mathematics Research Notices 2022(6), 4222-4258 (Oxford University Press) · 34 pages, 4 figures; v2 implements changes suggested by the referees; to appear in International Mathematics Research Notices
openalex created_date 2018/11/02 · arxiv created 2020/06/04 · openalex publication_date 2020/06/04 · arxiv updated 2021/01/29 · openalex updated_date 2026/08/05
Abstract We obtain several results for (iterated) planar contact manifolds in higher dimensions. (1) Iterated planar contact manifolds are not weakly symplectically co-fillable. This generalizes a 3D result of Etnyre [ 14] to a higher-dimensional setting, where the notion of weak fillability is that due to Massot-Niederkrüger-Wendl [ 38]. (2) They do not arise as nonseparating weak contact-type hypersurfaces in closed symplectic manifolds. This generalizes a result by Albers-Bramham-Wendl [ 4]. (3) They satisfy the Weinstein conjecture, that is, every contact form admits a closed Reeb orbit. This is proved by an alternative approach as that of [ 2] and is a higher-dimensional generalization of a result of Abbas-Cieliebak-Hofer [ 1]. The results follow as applications from a suitable symplectic handle attachment, which bears some independent interest.