Submanifolds in contact geometry

2025/10/07 by Etnyre, John B.
#FOS: Mathematics #Geometric Topology (math.GT) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2510.05804

Abstract

We survey what is known about various special types of submanifolds of contact manifolds and discuss their role in the development of contact geometry.

Citations

• Cable links of uniformly thick knot types
• Legendrian Hopf links in L(p,1)
• Existence and construction of non-loose knots
• Tight contact structures without symplectic fillings are everywhere
• Legendrian Torus and Cable Links
• Cabling Legendrian and transverse knots
• Non-simplicity of isocontact embeddings in all higher dimensions
• Iso-contact embeddings of manifolds in co-dimension 2
• Non-loose unknots, overtwisted discs, and the contact mapping class\n group of S³
• Cubic Planar Graphs and Legendrian Surface Theory
• Legendrian satellites
• Knot contact homology detects cabled, composite, and torus knots
• Transverse Surgery on Knots in Contact 3-Manifolds
• Existence and classification of overtwisted contact structures in all dimensions
• On the Legendrian and transverse classification of cablings
• On knots in overtwisted contact structures
• Legendrian torus knots in lens spaces
• Effect of Legendrian Surgery
• Rational linking and contact geometry
• Finitude homotopique et isotopique des structures de contact tendues
• Fibered Transverse Knots and the Bennequin Bound
• Heegaard Floer invariants of Legendrian knots in contact three--manifolds
• Topologically Trivial Legendrian Knots
• Legendrian Contact Homology in P X R
• Orientations in Legendrian Contact Homology and Exact Lagrangian Immersions
• Ozsvath-Szabo invariants and tight contact three-manifolds, III
• Legendrian and Transversal Knots
• On Symplectic Cobordisms
• Computable Legendrian invariants
• Tight contact structures with no symplectic fillings
• On the non-existence of tight contact structures
• Legendrian links of topological unknots

Related

• Some Special Geometry in Dimension Six
• Submanifolds of symplectic manifolds with contact border
• Géométrie de contact: de la dimension trois vers les dimensions supérieures
• Moment-angle manifolds, intersection of quadrics and higher dimensional contact manifolds
• Semi-invariant Submanifolds of Normal Complex Contact Metric Manifolds