Publications and Preprints

  1. Existence of coLegendrians in contact 5-manifolds, preprint 2020. Introduction of the 2nd gen Orange.

  2. A dynamical construction of Liouville domains, Proc. Amer. Math. Soc. (2020) This short note contains nothing particularly deep, but it contains every reason why I'm not yet bored with mathematics.

  3. (With K. Honda) Convex hypersurface theory in contact topology, preprint 2019. In this sequel to the paper right below, we lay the foundation of convex hypersurface theory. As immediate applications, we show the existence of compatible (partial) open book decompositions and (codim-2) contact submanifolds.

  4. (With K. Honda) Bypass attachments in higher-dimensional contact topology, preprint 2018. High (> 3) dimensional bypass attachment is constructed, as well as the overtwisted orange. As an application, we construct examples of overtwisted convex hypersurfaces.

  5. On plastikstufe, bordered Legendrian open book and overtwisted contact structures, J. Topol. (2017) We prove plastikstufe implies overtwistedness of the contact structure in any dimension. Moreover, we show in dimension 5 that bordered Legendrian open book (bLob) also implies overtwistedness.

  6. On Legendrian foliations in contact manifolds II: Deformation theory, preprint 2014. Third in the row. We study the coisotropic deformation problem for nonsingular Legendrian foliations. Some elementary applications in foliation theory are explored. Deformation theory of higher dimensional coisotropic submanifolds is also discussed.

  7. Non-existence of certain singularities in Legendrian foliations, preprint 2014. Second in the row. We study the the singular locus of Legendrian foliations in general. As a corollary, we show the Legendrian foliation uniquely determines the contact germ.

  8. On Legendrian foliations in contact manifolds I: Singularities and neighborhood theorems, Math. Res. Lett. (2015) This is the first of a series of papers devoted to understanding coisotropic submanifolds of higher dimensional contact manifolds. In this paper we study some basic properties of the characteristic foliation and prove a neighborhood theoreom analogous to Weinstein's neighborhood theorem in symplectic geometry.

  9. (With J. Ge) 1/4-Pinched Contact Sphere Theorem, Asian J. Math. (2016) We prove that a contact structure is universally tight if the compatible Riemannian metric is 1/4-pinched. This generalizes a result of Etnyre-Komendarczyk-Massot.

  10. (With V. Ramos) A topological grading on bordered Heegaard Floer homology, Quantum Topology (2015). This is a continuation of the work right below, which generalizes the grading by plane fields to bordered Heegaard Floer homology.

  11. (With V. Ramos) An absolute grading on Heegaard Floer homology by homotopy classes of oriented 2-plane fields, J. Symplectic Geom. (2016) We construct an absolute grading on Heegaard Floer homology using homotopy classes of plane fields. It is also shown that the grading is compatible with cobordism maps and contact invariants. In particular it recovers Ozsvath-Szabo's absolute Q-grading.

  12. Bypass attachments and homotopy classes of 2-plane fields in contact topology, J. Symplectic Geom. (2014). We show that the bypass triangle, in the sense of K. Honda, decreases the grading in the contact category by one.

  13. A proof of the classification theorem of overtwisted contact structures via convex surface theory, J. Symplectic Geom. (2013). We reprove the classification result of overtwisted contact structures due to Eliashberg, using convex surface theory and bypasses.