The plastikstufe -- a generalization of the overtwisted disk to higher dimensions

DOI10.2140/agt.2006.6.2473zbMath1129.53056arXivmath/0607610OpenAlexW2087539487MaRDI QIDQ863107

Klaus Niederkrüger

Publication date: 25 January 2007

Published in: Algebraic \& Geometric Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0607610

zbMATH Keywords

generalization of overtwistednessnonfillable contact manifolds of higher dimension

Mathematics Subject Classification ID

Symplectic and contact topology in high or arbitrary dimension (57R17) Global theory of symplectic and contact manifolds (53D35) Contact manifolds (general theory) (53D10)

Related Items

Existence and classification of overtwisted contact structures in all dimensions, Diffeomorphism type via aperiodicity in Reeb dynamics, An algebraic approach to the algebraic Weinstein conjecture, Making cobordisms symplectic, Symplectic cobordisms and the strong Weinstein conjecture, Weak and strong fillability of higher dimensional contact manifolds, Some remarks on the size of tubular neighborhoods in contact topology and fillability, Loose Legendrians and the plastikstufe, Towards a good definition of algebraically overtwisted, A hierarchy of local symplectic filling obstructions for contact 3-manifolds, Higher Dimensional Contact Topology via Holomorphic Disks, Gromov compactness for holomorphic discs with totally real boundary conditions, Sasaki structures distinguished by their basic Hodge numbers, THE WEINSTEIN CONJECTURE IN THE PRESENCE OF SUBMANIFOLDS HAVING A LEGENDRIAN FOLIATION, Tightness in contact metric 3-manifolds, Geometric criteria for overtwistedness, Almost contact 5-manifolds are contact, A class of non-fillable contact structures, Subcritical contact surgeries and the topology of symplectic fillings, CONTACT HOMOLOGY OF LEFT-HANDED STABILIZATIONS AND PLUMBING OF OPEN BOOKS, Recent advances in symplectic flexibility, On properties of Bourgeois contact structures, Exotic symplectic structures, The canonical contact structure on the link of a cusp singularity, The singular Weinstein conjecture, Quantitative Darboux theorems in contact geometry, Contact homology and virtual fundamental cycles, Bourgeois contact structures: tightness, fillability and applications

Cites Work

• A remarkable symplectic structure
• Une structure symplectique sur \({\mathbb{R}}^ 6\) avec une sphère lagrangienne plongée et un champ de Liouville complet. (A symplectic structure on \({\mathbb{R}}^ 6\) with an embedded Lagrange sphere and a complete Liouville field)
• Pseudo holomorphic curves in symplectic manifolds
• Elliptic partial differential equations of second order
• Classification of overtwisted contact structures on 3-manifolds
• A class of non-fillable contact structures
• The contact homology of Legendrian submanifolds in \(\mathbb R^{2n+1}\)
• Corrigenda to: Introduction to Symplectic Topology
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item