Ko Honda
Publications: Many
of
these are links to ArXiv, Geometry & Topology, or
Algebraic & Geometric Topology.
- (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,
preprint 2018.
- (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: July 13, 2019 |