Preprints
  
   

Preprints
  1. Lagrangian Realizations of Ribbon Cobordisms
    joint work with Caitlin Leverson, Preprint 2024.
  2. Symplectic rational homology ball fillings of Seifert fibered spaces
    joint work with Burak Ozbagci and Bulent Tosun, Preprint 2024.
  3. Existence and construction of non-loose knots
    joint work with Rima Chatterjee, Anubhav Mukherjee and Hyunki Min, Preprint 2023.
  4. Surgeries on the trefoil and symplectic fillings
    joint work with Nur Sa\={g}lam, Preprint 2023.
  5. Small symplectic caps and embeddings of homology balls in the complex projective plane
    joint work with Hyunki Min, Lisa Piccirillo and Agniva Roy, Preprint 2023.
  6. Non-loose torus knots
    joint work with Hyunki Min and Anubhav Mukherjee, Preprint 2022.
  7. Contact structures on 5-manifolds
    Preprint 2012.
  1. Stein traces and characterizing slopes
    joint work with Roger Casals and Marc Kegel, Math. Annalen 389 (2024), 1053--1098.
  2. Legendrian Torus and Cable Links
    joint work with Jennifer Dalton and Lisa Traynor, Journal of Symplectic Geometry 22 (2024), 11--108.
  3. Cabling Legendrian and transverse knots
    joint work with Apratim Chakraborty and Hyunki Min, Jounral of Differential Geom 126 (2024), 1--48.
  4. Generalizations of planar contact manifolds to higher dimensions
    joint work with Bahar Acu and Burak Ozbagci, Journal of Symplectic Geometry 21 (2023), 683--721.
  5. Homology spheres bounding acyclic smooth manifolds and symplectic fillings
    joint work with Bulent Tosun, Michigan Math.~J 73 (2023), 719--734.
  6. Contact surgery numbers
    joint work with Marc Kegel and Sinem Onaran, Journal of Symplectic Geometry 21 (2023), 1255--1333.
  7. On 3-manifolds that are boundaries of exotic 4-manifolds
    joint work with Hyunki Min and Anubhav Mukherjee, Trans.~Amer.~Math.~Soc 375 (2022), 4307--4332.
  8. Symplectic hats
    joint work with Marco Golla, Journal of Topology 15 (2022), 2216--2269.
  9. Symplectic fillings and cobordisms of lens spaces
    joint work with Agniva Roy, Trans.~Amer.~Math.~Soc. 374 (2021), 8813--8867.
  10. Symplectic fillings, contact surgeries, and Lagrangian disks
    joint work with James Conway and Bulent Tosun, IMRN 2021 no.~8 (2021), 6020--6050.
  11. Legendrian contact homology in $\mathbb{R}^3$
    joint work with Lenhard Ng, Surveys in Differential Geometry 25 (2020), 103-161.
  12. Non-simplicity of isocontact embeddings in all higher dimensions
    joint work with Roger Casals, GAFA 30 (2020), 1--33.
  13. Contact surgery and symplectic caps
    joint work with James Conway, Bulletin of the LMS 52 (2020), 379--394.
  14. Transverse universal links
    joint work with Roger Casals, Proc. Sympos. Pure Math. 102 (2019), 43--55.
  15. Embedding all contact $3$--manifolds in a fixed contact 5--manifold
    joint work with Yanki Lekili, Journal of the LMS (2) 99 (2019), 52--68.
  16. Legendrian satellites
    joint work with Vera V\'ertesi, IMRN 2018 no.~23 (2018), 7241--7304.
  17. Braided embeddings of contact 3-manifolds in the standard contact 5-sphere
    joint work with Ryo Furukawa, Journal of Topology 10 (2017), 412--446.
  18. Sutured Floer homology and invariants of Legendrian and transverse knots
    joint work with David Shea Vela-Vick and Rumen Zarev, Geometry and Topology 21 (2017), 1469--1582.
  19. Corrigendum to ``On generalizing Lutz twists"
    joint work with Dishant M Pancholi, J.~Lond.~Math.~Soc.\ (2) 94 (2016), 662--665.
  20. Quantitative Darboux theorems in contact geometry
    joint work with Rafal Komendarczyk and Patrick Massot, Trans.~Amer.~Math.~Soc 368 (2016), 7845--7881.
  21. Monoids in the mapping class group
    joint work with Jeremy Van Horn-Morris, Geometry and Topology Monographs 19 (2015), 319--365.
  22. The arc complex and contact geometry, non-destabilizable planar open book decompositions of the tight contact 3-sphere
    joint work with Youlin Li, IMRN 2015 (2015), 1401--1420.
  23. Admissible transverse surgery does not preserve tightness
    joint work with John A Baldwin, Math. Annalen 357 (2013), 441--468.
  24. Knot contact homology
    joint work with Tobias Ekholm, Lenhard Ng and Michael G. Sullivan, Geometry and Topology 17 (2013), 975--1112.
  25. On knots in overtwisted contact structures
    Journal of Quantum Topology 4 (2013), 229--264.
  26. Filtrations on the knot contact homology of transverse knots
    joint work with Tobias Ekholm, Lenhard Ng and Michael G. Sullivan, Math. Annalen 355 (2013), 1561--1591.
  27. Legendrian and transverse twist knots
    joint work with Lenhard Ng and Vera V\'ertesi, J.\ European Math.\ Soc. 15 (2013), 969--995.
  28. Legendrian and transverse cables of positive torus knots
    joint work with Douglas J. LaFountain and Bulent Tosun, Geometry and Topology 16 (2012), 1639--1689.
  29. Tightness in contact metric 3--manifolds
    joint work with Rafal Komendarczyk and Patrick Massot, Invent. Math. 188 (2012), 621--657.
  30. Cabling, contact structures and mapping class monoids
    joint work with Kenneth L Baker and Jeremy Van Horn-Morris, J.\ Differential Geom 90 (2012), 1--80.
  31. Rational linking and contact geometry
    joint work with Kenneth L Baker, Progr. Math. 296 (2012), 19--37.
  32. Fibered Transverse Knots and the Bennequin Bound
    joint work with Jeremy Van Horn-Morris, IMRN 2011 (2011), 1483--1509.
  33. Product Structures for Legendrian Contact Homology
    joint work with Gokhan Civan, Paul Koprowski, Joshua Sabloff and Alden Walker, Math.\ Proc.\ Cambridge Philos.\ Soc. 150 (2011), 291--311.
  34. On generalized Lutz twists
    joint work with Dishant M Pancholi, Proc.\ of the LMS 84 (2011), 670--688.
  35. Torsion and Open Book Decompositions
    joint work with David Shea Vela-Vick, IMRN 2010 (2010), 4385--4398.
  36. A note on the support norm of a contact structure
    joint work with John A Baldwin, Proc. Sympos. Pure Math. 82 (2009), 79--88.
  37. A Duality Exact Sequence for Legendrian Contact Homology
    joint work with Tobias Ekholm and Joshua Sabloff, Duke Math.\ J. 150 (2009), 1--75.
  38. Lectures on contact geometry in low-dimensional topology
    Low dimensional topology (IAS/Park City Math. Ser., 15), 2009229--264.
  39. A note on Stein fillings of contact manifolds
    joint work with Anar Akhmedov, Thomas E. Mark and Ivan Smith, MRL 15 (2008), 1127--1132.
  40. On contact surgery
    Proc.~Amer.~Math.~Soc. 136 (2008), 3355--3362.
  41. Invariants of contact structures from open books
    joint work with Burak Ozbagci, Trans.~Amer.~Math.~Soc 260 (2008), 3133--3151.
  42. Contact structures on 3-manifolds are deformations of foliations
    MRL 14 (2007), 775-779.
  43. Legendrian Contact Homology in $P\times\R$
    joint work with Tobias Ekholm and Michael G. Sullivan, Trans.~Amer.~Math.~Soc 359 (2007), 3301--3335.
  44. Open books and plumbings
    joint work with Burak Ozbagci, IMRN 2006 (2006), 1--17.
  45. Realizing 4-manifolds as achiral Lefschetz fibrations
    joint work with Terry Fuller, IMRN 2006 (2006), 1--21.
  46. Contact Manifolds
    Encyclopedia of Mathematical Physics, eds. J.-P. Fran\c{c}oise, G.L. Naber and S.T. Tsou, Oxford: Elsevier, v. 1 2006631--636.
  47. Lectures on open book decompositions and contact structures
    Clay Math. Proc. 5 (the proceedings of the ``Floer Homology, Gauge Theory, and Low Dimensional Topology Workshop''), 2006103--141.
  48. Invariants of Knots, Embeddings and Immersions via Contact Geometry
    joint work with Tobias Ekholm, Fields Inst. Commun. 47 (2005), 77--96.
  49. Cabling and transverse simplicity
    joint work with Ko Honda, Annals of Math 162 (2005), 1305-1333.
  50. Generic hydrodynamic instability of curl eigenfields
    joint work with Robert Ghrist, SIAM J. Appl. Dyn. Syst. 4 (2005), no. 2, 377-390.
  51. Orientations in Legendrian Contact Homology and Exact Lagrangian Immersions
    joint work with Tobias Ekholm and Michael G. Sullivan, IJM 16 (2005), no. 5, 453-532.
  52. Legendrian and Transversal Knots
    in the Handbook of Knot Theory (Elsevier B. V., Amsterdam), 2005105-185.
  53. The Contact Homology of Legendrian Submanifolds in $\R^{2n+1}$
    joint work with Tobias Ekholm and Michael G. Sullivan, J. Differential Geom. 71 (2005), no. 2, 177-305.
  54. Non-isotopic Legendrian Submanifolds in $\R^{2n+1}$
    joint work with Tobias Ekholm and Michael G. Sullivan, J. Differential Geom. 71 (2005), no. 1, 85-128.
  55. Planar open book decompositions and contact structures
    IMRN 2004 (2004), no. 79, 4255-4267.
  56. On Symplectic Fillings
    Algebr. Geom. Topol. 4 (2004), 73-80.
  57. On connected sums and Legendrian knots
    joint work with Ko Honda, Adv. Math. 179 (2003), 59-74.
  58. Introductory Lectures on Contact Geometry
    Proc. Sympos. Pure Math. 71 (2003), 81-107.
  59. Problems in Low Dimensional Contact Topology
    joint work with Lenhard Ng, Proc. Sympos. Pure Math. 71 (2003), 337-357.
  60. Tight contact structures and Anosov flows
    joint work with Robert Ghrist, Topol. and its Appl. 124 (2002), 211-219.
  61. Invariants of Legendrian knots and coherent orientations
    joint work with Lenhard Ng and Joshua Sabloff, J. Sympl. Geom. 1 (2002), no. 2, 321-368.
  62. Contact topology and hydrodynamics II solid tori
    joint work with Robert Ghrist, Ergod. Th. \& Dynam. Sys. 22 (2002), 819-833.
  63. Tight contact structures with no symplectic fillings
    joint work with Ko Honda, Invent. Math. 148 (2002), no. 3, 609-626.
  64. On Symplectic Cobordisms
    joint work with Ko Honda, Math. Annalen 323 (2002), no. 1, 31-39.
  65. Knots and contact geometry I torus knots and the figure eight knot
    joint work with Ko Honda, J. Sympl. Geom. 1 (2001), no. 1, 63-120.
  66. An index for closed orbits in Beltrami fields
    joint work with Robert Ghrist, Phys. D 159 (2001), no. 3-4, 180-189.
  67. Erratum to tight contact structures on lens spaces
    Commun. Contemp. Math. 3 (2001), no. 4, 649-652.
  68. On the nonexistence of tight contact structures
    joint work with Ko Honda, Ann. of Math. (2) 153 (2001), no. 3, 749-766.
  69. Tight contact structures on lens spaces
    Commun. in Contemp. Math. 2 (2000), no. 4, 559-577.
  70. Contact topology and hydrodynamics III knotted orbits
    joint work with Robert Ghrist, Trans. Amer. Math. Soc. 352 (2000), 5781-5794.
  71. Contact topology and hydrodynamics I Beltrami fields and the Seifert Conjecture
    joint work with Robert Ghrist, Nonlinearity 13 (2000), 441-458.
  72. Stratified integrals and unknots in invicid flows
    joint work with Robert Ghrist, Contemp. Math. 246 (1999), 99-111.
  73. Gradient flows within plane fields
    joint work with Robert Ghrist, Comm. Math. Helvetici 74 (1999), 507-529.
  74. Tight contact structures via dynamics
    joint work with Robert Ghrist, Proceedings of the AMS 127 (1999), 3697-3706.
  75. Transversal torus knots
    Geometry and Topology 3 (1999), 253-268.
  76. Symplectic convexity in low-dimensional topology
    Topol. and its Appl. 88 (1998), 3-25.
  77. Smooth structures on collarable ends of 4-manifolds
    joint work with Zarko Bizaka, Topology 37 (1998), 461-467.
  78. Symplectic constructions on 4-manifolds
    Dissertation, University of Texas (December 1996), 1-92.