Legendrian knots, transverse knots and combinatorial Floer homology

2006/11/30 by Peter Ozsváth, Peter Ozsvath, Zoltán Szabó +3 · 5 citations
Mathematics · #Advanced Combinatorial Mathematics #Algebra over a field #Anatomy #Biology #Cellular homology #Combinatorics #Floer homology #Geometric and Algebraic Topology #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Invariant (physics) #Khovanov homology #Knot (papermaking) #Knot invariant #Knot theory #Mathematical physics #Mathematics #Morse homology #Pure mathematics #Symplectic geometry #Transverse plane #math.GT #math.SG #msc:57M25 #msc:57R17 #msc:57R58

paper · pdf · doi:10.2140/gt.2008.12.941

published as Geom. Topol. 12 (2008) 941-980 · 27 pages, 13 figures; v2: Expand and correct discussion of links

arxiv created 2008/01/04 · openalex publication_date 2008/05/12 · arxiv updated 2014/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Using the combinatorial approach to knot Floer homology, we define an invariant for Legendrian knots (or links) in the three-sphere, with values in knot Floer homology. This invariant can also be used to construct an invariant of transverse knots. 53D12, 57R17, 57R58; 57M25

Citations

• Floer homology and knot complements
• Holomorphic disks and knot invariants
• On combinatorial link Floer homology
• Khovanov homology and the slice genus

Cited by

• Bennequin Type Inequalities in Lens Spaces
• Product Structures for Legendrian Contact Homology
• The knot Floer complex and the smooth concordance group
• Comparing Bennequin-type inequalities
• Rectangular diagrams of surfaces: distinguishing Legendrian knots