Ko Honda

Publications:  Many of these are links to ArXiv, Geometry & Topology, or Algebraic & Geometric Topology.  All the files which can be downloaded directly from this page are now pdf files.
 

1. (With V. Colin and P. Ghiggini) HF=ECH via open book decompositions: a summary, preprint 2011.  This is a brief summary of our proof that HF=ECH.  The main papers are still in progress.
   
2. (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.
   
3. (With V. Colin, P. Ghiggini and M. Hutchings) Sutures and contact homology I, preprint 2010.  We define the sutured versions of contact homology (in any dimension) and embedded contact homology (in dimension three).
   
4. (With V. Colin) Reeb vector fields and open book decompositions, preprint 2008.  We compute parts of the contact homology of contact 3-manifolds which are supported by open books with pseudo-Anosov monodromy.
   
5. (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.
   
6. (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. 
   
7. (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.
   
8. (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.
   
9. (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.
   
10. (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".
    
11. (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.
12. (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.
    
13. (With W. Kazez and G. Matić)  Right-veering diffeomorphisms of a compact surface 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.
    
14. The topology and geometry of contact structures in dimension three, ICM 2006 proceedings.
    
15. (With W. Kazez and G. Matić)  Right-veering diffeomorphisms of a compact surface with boundary, Invent. Math. (2007).  We give a criterion for a contact structure to be tight in the open book framework of Giroux.
    
16. (With W. Kazez and G. Matić) Pinwheels and bypasses, Algebr. Geom. Topol. (2005). (arXiv version)
    
17. (With V. Colin) Constructions contrôlées de champs de Reeb et applications, Geom. Topol. (2005). (arXiv version) 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).
    
18. 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.
    
19. (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.
20. (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".)
21. (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.
22. (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.  
23. (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.
24. (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....
25. 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. 
26. (With J. Etnyre) On symplectic cobordisms, Math. Ann. (2002).  A short note on concave symplectic fillings and symplectic cobordisms.
27. (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!
28. (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.
29. 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. 
30. (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. 
31. (With W. Kazez and G. Matić) Tight contact structures and taut foliations, Geom. Topol. (2000). (arXiv version)  We unite sutured manifolds and their decompositions with their siblings, the `convex structures' and their decompositions.
32. (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.
33. 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''. 
34. On the classification of tight contact structures I, Geom. Topol. (2000). (arXiv version)  Classifies tight contact structures on lens spaces, solid tori, and T^2 \times I.
    
35. 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).
36. 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'. 
37. 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. 
38. 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.
39. 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.
40. On harmonic forms for generic metrics, Ph.D. Thesis.