Ko Honda
Mathematics · UCLA
Publications
2024–2026
1
Higher-dimensional Heegaard Floer homology and spectral networks
With Y. Tian and T. Yuan·Preprint, 2026
New
2
Towards a symplectic Khovanov homology for links in fibered 3-manifolds
With V. Colin and Y. Tian·Preprint, 2025
A Khovanov-type invariant of a transverse link in a fibered 3-manifold.
3
Morse theory of loop spaces and Hecke algebras
With R. Krutowski, Y. Tian and T. Yuan·Preprint, 2025
4
Sutured Heegaard Floer and embedded contact homologies are isomorphic
With V. Colin and P. Ghiggini·J. Eur. Math. Soc., to appear
The sutured version of the HF=ECH correspondence.
5
The equivalence of Heegaard Floer homology and embedded contact homology via open book decompositions I
With V. Colin and P. Ghiggini·Inst. Hautes Études Sci. Publ. Math. (2024)
6
The equivalence of Heegaard Floer homology and embedded contact homology via open book decompositions II
With V. Colin and P. Ghiggini·Inst. Hautes Études Sci. Publ. Math. (2024)
7
The equivalence of Heegaard Floer homology and embedded contact homology III: from hat to plus
With V. Colin and P. Ghiggini·Inst. Hautes Études Sci. Publ. Math. (2024)
8
Applications of higher-dimensional Heegaard Floer homology to contact topology
With V. Colin and Y. Tian·J. Topol. (2024)
9
Embedded contact homology and open book decompositions
With V. Colin and P. Ghiggini·Geom. Topol. (2025)
First in the series on the equivalence of Heegaard Floer homology and embedded contact homology.
2018–2023
10
The Giroux correspondence in arbitrary dimensions
With J. Breen and Y. Huang·Preprint, 2023
Current working version (to be updated on arXiv later).
11
Higher-dimensional Heegaard Floer homology and Hecke algebras
With Y. Tian and T. Yuan·J. Eur. Math. Soc., to appear
12
Semi-global Kuranishi charts and the definition of contact homology
With E. Bao·Adv. Math. (2023)
Proves in full generality that contact homology is defined.
13
Foliations, contact structures and their interactions in dimension three
With V. Colin·Surv. Differ. Geom. (2022)
Survey with emphasis on sutured manifolds and invariants of sutured contact manifolds; includes new results.
14
Contact categories of disks
With Y. Tian·J. Symplectic Geom. (2022)
First paper describing the contact category.
15
Equivariant Lagrangian Floer cohomology via semi-global Kuranishi structures
With E. Bao·Algebr. Geom. Topol. (2021)
16
An exposition of the equivalence of Heegaard Floer homology and embedded contact homology
With V. Colin and P. Ghiggini·Contemp. Math. (2020)
17
Convex hypersurface theory in contact topology
With Y. Huang·Preprint, 2019
Proves C⁰-genericity of convex hypersurfaces. Current working version.
18
Topological entropy for Reeb vector fields in dimension three via open book decompositions
With M. Alves and V. Colin·J. Éc. Polytech. Math. (2019)
19
Bypass attachments in higher-dimensional contact topology
With Y. Huang·Preprint, 2018
Sequel to the convex hypersurface theory paper above.
20
Definition of cylindrical contact homology in dimension three
With E. Bao·J. Topol. (2018)
2010–2017
21
Legendrian knots and exact Lagrangian cobordisms
With T. Ekholm and T. Kálmán·J. Eur. Math. Soc. (2016)
22
Equivalence of Heegaard Floer homology and embedded contact homology via open book decompositions
With V. Colin and P. Ghiggini·Proc. Nat. Acad. Sci. (2011)
Brief summary of the proof that HF=ECH.
23
Sutures and contact homology I
With V. Colin, P. Ghiggini and M. Hutchings·Geom. Topol. (2011)
Defines sutured versions of contact homology (any dimension) and embedded contact homology (dimension 3).
2007–2009
24
Reeb vector fields and open book decompositions
With V. Colin·J. Eur. Math. Soc. (2013)
Computes parts of the contact homology of contact 3-manifolds supported by open books with pseudo-Anosov monodromy.
25
On the flux of pseudo-Anosov homeomorphisms
With V. Colin and F. Laudenbach·Algebr. Geom. Topol. (2008)
Companion to "Reeb vector fields and open book decompositions." Exhibits a pseudo-Anosov homeomorphism acting trivially on first homology with nonzero flux.
26
Contact structures, sutured Floer homology and TQFT
With W. Kazez and G. Matić·Preprint, 2008
Defines a natural tensor product map in sutured Floer homology via gluing of sutured manifolds.
27
Finitude homotopique et isotopique des structures de contact tendues
With V. Colin and E. Giroux·Inst. Hautes Études Sci. Publ. Math. (2009)
Finiteness of tight contact structures on 3-manifolds. See also: Notes on the isotopy finiteness and On the coarse classification of tight contact structures.
28
Giroux torsion and twisted coefficients
With P. Ghiggini·Preprint, 2008
Calculates the effect of adding Giroux torsion for the Ozsváth–Szabó contact invariant with twisted coefficients.
29
The vanishing of the contact invariant in the presence of torsion
With P. Ghiggini and J. Van Horn-Morris·Preprint, 2007
Proves that the Ozsváth–Szabó contact invariant vanishes (ℤ-coefficients) when Giroux torsion is at least 2π.
30
Stabilizing the monodromy map of an open book decomposition
With V. Colin·Geom. Dedicata (2008)
Any mapping class on a compact oriented surface with nonempty boundary can be made pseudo-Anosov and right-veering after a sequence of positive stabilizations.
31
The contact invariant in sutured Floer homology
With W. Kazez and G. Matić·Invent. Math. (2008)
An invariant of a contact 3-manifold with convex boundary as an element of Juhász's sutured Floer homology.
32
On the contact class in Heegaard Floer homology
With W. Kazez and G. Matić·J. Differential Geom. (2009)
An alternate, more natural description of the contact class in the open book setting.
33
Right-veering diffeomorphisms of compact surfaces with boundary II
With W. Kazez and G. Matić·Geom. Topol. (2008)
Continues "Right-veering I"; further study of the difference between positive Dehn twist products and right-veering diffeomorphisms.
2004–2007
34
The topology and geometry of contact structures in dimension three
Ko Honda·ICM 2006 Proceedings
35
Right-veering diffeomorphisms of compact surfaces with boundary
With W. Kazez and G. Matić·Invent. Math. (2007)
A criterion for a contact structure to be tight in the open book framework of Giroux.
36
Pinwheels and bypasses
With W. Kazez and G. Matić·Algebr. Geom. Topol. (2005)
37
Constructions contrôlées de champs de Reeb et applications
With V. Colin·Geom. Topol. (2005)
Constructs hypertight Reeb vector fields — those with no contractible periodic orbits.
38
3-dimensional methods in contact geometry
Ko Honda·Different Faces of Geometry (Donaldson, Eliashberg, Gromov, eds.)
Lecture notes on the cut-and-paste theory of contact 3-manifolds.
39
Cabling and transverse simplicity
With J. Etnyre·Ann. of Math. (2005)
Examples of knot types that are not transversely simple.
40
Local properties of self-dual harmonic 2-forms on a 4-manifold
Ko Honda·J. Reine Angew. Math. (2004)
41
Transversality theorems for harmonic forms
Ko Honda·Rocky Mountain J. Math. (2004)
42
On the Gabai–Eliashberg–Thurston theorem
With W. Kazez and G. Matić·Comment. Math. Helv. (2004)
A purely 3-dimensional reproof that a closed, oriented, irreducible 3-manifold with nonzero H₂ carries a universally tight contact structure.
2000–2003
43
On connected sums and Legendrian knots
With J. Etnyre·Adv. Math. (2003)
Structure theorem for Legendrian knots under the connected sum operation.
44
Tight contact structures on fibered hyperbolic 3-manifolds
With W. Kazez and G. Matić·J. Differential Geom. (2003)
Classification of tight contact structures in the extremal case on surface bundles with pseudo-Anosov monodromy.
45
On symplectic cobordisms
With J. Etnyre·Math. Ann. (2002)
A short note on concave symplectic fillings and symplectic cobordisms.
46
Convex decomposition theory
With W. Kazez and G. Matić·Int. Math. Res. Not. (2002)
Proves existence of universally tight contact structures on "large" 3-manifolds; a toroidal 3-manifold carries infinitely many isomorphism classes of universally tight contact structures.
47
Tight contact structures with no symplectic fillings
With J. Etnyre·Invent. Math. (2002)
First example of a tight contact structure that is not weakly symplectically semi-fillable.
48
Gluing tight contact structures
Ko Honda·Duke Math. J. (2002)
A purely 3-dimensional gluing theorem with an application to Legendrian surgery.
49
Factoring nonrotative T² × I layers
Ko Honda·Geom. Topol. (2001)
Corrigendum for the Tight Structures I paper and subsequently propagated errors.
50
On the nonexistence of tight contact structures
With J. Etnyre·Ann. of Math. (2001)
The Poincaré homology sphere with reverse orientation has no positive contact structure.
51
Knots and contact geometry I: torus knots and the figure eight knot
With J. Etnyre·J. Symplectic Geom. (2001)
Lays groundwork for classifying Legendrian and transversal knots; completely classifies Legendrian torus knots and the figure eight knot.
1999–2000
52
Tight contact structures and taut foliations
With W. Kazez and G. Matić·Geom. Topol. (2000)
Unites sutured manifolds and their decompositions with convex structures and their decompositions.
53
On the classification of tight contact structures II
Ko Honda·J. Differential Geom. (2000)
Classifies tight contact structures on torus bundles over the circle and circle bundles over closed oriented surfaces.
54
On the classification of tight contact structures I
Ko Honda·Geom. Topol. (2000)
Classifies tight contact structures on lens spaces, solid tori, and T² × I.
55
An openness theorem for harmonic 2-forms on 4-manifolds
Ko Honda·Illinois J. Math. (2000)
56
A note on Morse theory of harmonic forms
Ko Honda·Topology (1999)
Thesis & other
57
Notes on the isotopy finiteness
With V. Colin and E. Giroux·Informal notes
Isotopy finiteness of tight contact structures on atoroidal 3-manifolds.
58
On the coarse classification of tight contact structures
With V. Colin and E. Giroux·Georgia International Topology Conference, 2001
59
Confoliations transverse to vector fields
Ko Honda·Preliminary version
Characterizes which nonsingular Morse–Smale flows are tangent to contact structures; addresses a question of Arnold.
60
On harmonic forms for generic metrics
Ko Honda·Ph.D. Thesis