Ko Honda
Publications
- (With Y. Tian and
T. Yuan) Higher-dimensional Heegaard Floer homology and
Hecke algebras, preprint 2022.
- (With V. Colin and
Y. Tian)
Applications of higher-dimensional Heegaard Floer homology
to contact topology, preprint 2020.
- (With V. Colin and
P. Ghiggini) An exposition of the equivalence of Heegaard
Floer homology and embedded contact homology,
preprint 2020.
- (With Y. Huang) Convex
hypersurface theory in contact topology, preprint
2019. We prove the C^0-genericity of convex hypersurfaces.
- (With E. Bao) Equivariant
Lagrangian Floer cohomology via semi-global Kuranishi
structures, Algebr. Geom. Topol, to appear.
- (With V. Colin) Foliations,
contact structures and their interactions in dimension three,
preprint 2018. A survey with an emphasis on sutured
manifolds and invariants of sutured contact manifolds.
There are also some new results in the paper.
- (With Y. Huang) Bypass
attachments in higher-dimensional contact topology,
preprint 2018. Although we wrote this first, this should
be viewed as the sequel to the convex hypersurface theory paper
above.
- (With M. Alves and
V. Colin) Topological
entropy for Reeb vector fields in dimension three via open
book decompositions, J. Ecole Poly., to appear.
- (With Y. Tian) Contact categories
of disks, preprint 2016. The first paper where
the contact category is described.
- (With E. Bao) Semi-global
Kuranishi charts and the definition of contact homology,
preprint 2015. We prove in general that contact homology
is defined.
- (With E. Bao) Definition
of cylindrical contact homology in dimension three,
J. Topol. (2018). We give the definition of contact
homology in a special case.
- (With T. Ekholm and
T. Kálmán) Legendrian knots and exact Lagrangian cobordisms,
J. Eur. Math. Soc. (2016).
- (With V. Colin and
P. Ghiggini) The equivalence of Heegaard Floer homology and
embedded contact homology via open book decompositions I, preprint 2012.
- (With V. Colin and
P. Ghiggini) The equivalence of Heegaard Floer homology and
embedded contact homology via open book decompositions II, preprint 2012.
- (With V. Colin and
P. Ghiggini) The equivalence of Heegaard Floer homology and
embedded contact homology III: from hat to plus, preprint 2012.
- (With V. Colin and
P. Ghiggini) Equivalence of Heegaard Floer homology and embedded
contact homology via open book decompositions,
Proc. Nat. Acad. Sci. (2011). This is a brief summary of
our proof that HF=ECH.
- (With V. Colin and
P. Ghiggini) Embedded contact homology and open book
decompositions, preprint 2010. This is the
first of a series of papers devoted to the equivalence of
Heegaard Floer homology and embedded contact homology.
- (With V. Colin, P.
Ghiggini and M. Hutchings) Sutures and contact
homology I, Geom. Topol. (2011). We define the
sutured versions of contact homology (in any dimension) and
embedded contact homology (in dimension three).
- (With V. Colin) Reeb
vector fields and open book decompositions, J.
Eur. Math. Soc. (2013). We compute parts of the contact
homology of contact 3-manifolds which are supported by open
books with pseudo-Anosov monodromy.
- (With V. Colin and F.
Laudenbach) On the flux of
pseudo-Anosov homeomorphisms, Algebr. Geom. Topol.
(2008). This is a companion paper to "Reeb vector fields
and open book decompositions". Here we exhibit a
pseudo-Anosov homeomorphism which acts trivially on first
homology and has nonzero flux.
- (With W. Kazez and G.
Matić) Contact structures,
sutured Floer homology and TQFT, preprint
2008. This is in some sense a sequel to "The contact
invariant in sutured Floer homology". We define a natural
tensor product map in sutured Floer homology, obtained by gluing
sutured manifolds, and look at some consequences.
- (With V. Colin and E.
Giroux) Finitude
homotopique et isotopique des structures de contact tendues,
Inst. Hautes Études Sci. Publ. Math. (2009). This
is the long-promised text concerning the finiteness of tight
contact structures on 3-manifolds. There are related texts
Notes on the isotopy
finiteness and On
the coarse classification of tight contact structures.
- (With P. Ghiggini) Giroux torsion and twisted
coefficients, preprint 2008. This is an
improvement of the paper right below, in the sense we calculate
the effect of adding "Giroux torsion" for the Ozsvath-Szabo
contact invariant with respect to a twisted coefficient system.
- (With P. Ghiggini and
J. Van Horn-Morris) The
vanishing of the contact invariant in the presence of
torsion, preprint 2007. We prove that, with
Z-coefficients, the Ozsvath-Szabo contact invariant in Heegaard
Floer homology vanishes if its "Giroux torsion" is at least 2\pi.
- (With V. Colin) Stabilizing the monodromy map
of an open book decomposition, Geom. Dedicata
(2008). We show that 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. This is a spinoff of our paper "Reeb
vector fields and open book decompositions".
- (With W. Kazez and G.
Matić) The contact
invariant in sutured Floer homology, Invent.
Math. (2008). We describe an invariant of a contact
3-manifold with convex boundary as an element of Juhasz's
sutured Floer homology. It specializes to Ozsvath-Szabo's
contact invariant in Heegaard Floer homology, via the paper
right below on Heegaard Floer homology.
- (With W. Kazez
and G. Matić) On the
contact class in Heegaard Floer homology,
J. Differential Geom. (2009). We give an alternate
description of the contact class in Heegaard Floer homology,
which is more natural in the open book setting.
- (With W. Kazez
and G. Matić) Right-veering
diffeomorphisms
of
compact surfaces with boundary II, Geom. Topol.
(2008). This is a continuation of "Right-veering I"
below; we continue to study the difference between the monoid of
products of positive Dehn twists and the monoid of right-veering
diffeomorphisms.
- The
topology and geometry of contact structures in dimension
three, ICM 2006 proceedings.
- (With W. Kazez
and G. Matić) Right-veering
diffeomorphisms
of
compact surfaces with boundary, Invent. Math.
(2007). We give a criterion for a contact structure to be
tight in the open book framework of Giroux.
- (With W. Kazez
and G. Matić) Pinwheels and
bypasses, Algebr. Geom. Topol. (2005).
- (With V. Colin) Constructions contrôlées de
champs de Reeb et applications, Geom. Topol.
(2005). We construct Reeb vector fields on contact manifolds
which don't have any contractible periodic orbits. Such
Reeb vector fields, called hypertight
Reeb vector fields, are particularly nice because we can do
cylindrical contact homology (instead of the more complicated
general theory).
- 3-dimensional
methods in contact geometry, in "Different Faces of
Geometry", Donaldson, Eliashberg, Gromov, eds. These are
lecture notes on the cut-and-paste theory of contact
3-manifolds.
- (With
J.
Etnyre) Cabling and transverse simplicity, Ann.
of Math. (2005). These give examples of knot types which
are not transversely simple, i.e., there are transverse knots
with the same topological knot type and self-linking number
which are not contact isotopic.
- (With
J.
Etnyre) On connected sums and Legendrian knots,
Adv. Math. (2003) This gives the structure theorem for
Legendrian knots under the connected sum operation.
(This was formerly known as ``Knots and contact geometry II:
connected sums".)
- (With
V.
Colin and E. Giroux) Notes on the isotopy finiteness,
an informal set of notes (in English) on the isotopy
finiteness of tight contact structures on atoroidal
3-manifolds. The final version (in French) is still in
preparation.
- (With
V.
Colin and E. Giroux) On the coarse classification of
tight contact structures, Topology of
Manifolds (Proceedings of the 2001 Georgia International
Topology Conference), Matic and McCrory eds. This is a
sketch of the finiteness theorems --- I think there are
enough details for the homotopy finiteness that someone
relatively well-versed in contact topology should(?) be able
to fill in the details.
- (With
W.
Kazez and G. Matić) Tight contact structures on fibered
hyperbolic 3-manifolds, J. Differential Geom.
(2003). A classification of tight contact structures in
the extremal case on surface bundles which fiber over the
circle with pseudo-Anosov monodromy.
- (With
W.
Kazez and G. Matić) On the Gabai-Eliashberg-Thurston
theorem, Comment. Math. Helv. (2004). We
finally finish reproving, using purely three-dimensional
methods, the theorem of Gabai-Eliashberg-Thurston which states
that a closed, oriented, irreducible 3-manifold with nonzero
second homology carries a universally tight contact
structure. This and its evil twin above took much longer
than expected....
- Factoring
nonrotative T^2 x I layers, Geom. Topol.
(2001). This is actually a corrigendum for the Tight
Str. I paper and some mistakes which were propagated
subseqently.
- (With
J.
Etnyre) On symplectic cobordisms, Math. Ann.
(2002). A short note on concave symplectic fillings and
symplectic cobordisms.
- (With
W.
Kazez and G. Matić) Convex decomposition theory,
Int. Math. Res. Not. (2002). A continuation of Tight
contact structures and taut foliations. Here we prove
the existence of universally tight contact structures on
3-manifolds which are `large', in a completely 3-dimensional
manner. We do not use the theorems of
Eliashberg-Thurston on perturbing foliations into contact
structures and Eliashberg-Gromov on the tightness of a
symplectically fillable contact manifold. We also prove
that a toridal 3-manifold carries infinitely many isomorphism
classes of universally tight contact structures.
Hopefully appearing soon: its sequel!
- (With
J.
Etnyre) Tight contact structures with no symplectic
fillings, Invent. Math. (2002). This is the
first example of a tight contact structure which is not weakly
symplectically semi-fillable.
- Gluing
tight
contact structures, Duke Math. J. (2002).
This one's my attempt at producing a purely 3-dimensional
gluing theorem. This has an interesting application to
Legendrian surgery.
- (With
J.
Etnyre) Knots and contact geometry I: torus knots and
the figure eight knot, J. Symplectic Geom.
(2001). We lay the groundwork for classifying Legendrian
and transversal knots in general, and completely classify
Legendrian (and transversal) torus knots and the figure eight
knot.
- (With
W. Kazez and G. Matić) Tight contact structures and taut
foliations, Geom. Topol. (2000). We unite
sutured manifolds and their decompositions with their
siblings, the `convex structures' and their decompositions.
- (With
J.
Etnyre) On the nonexistence of tight contact structures,
Ann. of Math. (2001). The Poincare homology sphere with
reverse orientation has no positive contact structure.
- On the
classification of tight contact structures II, J. Differential Geom. (2000). Classifies tight
contact structures on torus bundles over the circle and circle
bundles over closed oriented surfaces. This was formerly two
preprints which were called ``On the classification of tight
contact structures II'' and ``On the classification of tight
contact structures III''.
- On
the classification of tight contact structures I, Geom. Topol. (2000). Classifies tight contact
structures on lens spaces, solid tori, and T^2 \times I.
- Confoliations
transverse to vector fields. This is a preliminary
version. The statements of theorems are not quite correct
(pointed out by Atsushi Sato). I am (VERY SLOWLY) trying
to fix the problem and working on a revised version in which I
characterize which nonsingular Morse-Smale flows are tangent
to contact structures, thereby answering a question posed by
Arnold (and worked on by Eliashberg and Thurston).
- Local properties of
self-dual harmonic 2-forms on a 4-manifold, J.
Reine Angew. Math. (2004). Short note describing almost
everything (not much) I understood about these `singular
symplectic forms'.
- Transversality
theorems for harmonic forms, Rocky Mountain J.
Math. (2004). I prove genericity theorems for harmonic
1, 2, and (n-1)-forms which clearly hold if we assume our
forms were only closed.
- An openness theorem
for harmonic 2-forms on 4-manifolds, Illinois J.
of Math (2000). An attempt at trying to understand,
intrinsically, what it means for a closed 2-form to be
harmonic.
- A note on Morse
theory of harmonic forms, Topology (1999).
An attempt at doing Morse-Novikov theory using harmonic
1-forms, instead of closed 1-forms.
- On harmonic forms
for generic metrics, Ph.D. Thesis.
Last modified: March 7, 2022 |