Publications:

  1. Immersed essential surfaces in hyperbolic 3-manifolds.  Comm. Anal. Geom. 10 (2002), 275--290.
  2. Boundary curves of surfaces with 4-plane property.      Geometry & Topology, 6 (2002), 609--647.
  3. Laminar branched surfaces in 3-manifolds.               Geometry & Topology, 6 (2002), 153--194.
  4. Commutator groups and foliations without holonomy.    Proc. Amer. Math. Soc. 130 (2002), 2471--2477.
  5. Boundary train tracks of laminar branched surfaces    Proc. of Symposia in Pure Math., 71, AMS (2003), 269--285.
  6. An algorithm to detect laminar 3-manifolds. (with Ian Agol)  Geometry & Topology, 7 (2003), 287--309.  
  7. Property P for knots admitting certain Gabai disks.     (with Oliver Dasbach)  Topology and its Applications, 142, (2004) 113--129.
  8. The Waldhausen conjecture (a 4-page outline of the proof of the Waldhausen conjecture) Oberwolfach Report 2005.
  9. An algorithm to find vertical tori in small Seifert fiber spaces.         Commertarii Mathematici Helvetici, 81 (2006) 727--753.
  10. Heegaard surfaces and measured laminations, I: the Waldhausen conjecture  Invent. Math. 167 (2007) 135 177   (arXiv:math.GT/0408198)
  11. Heegaard surfaces and measured laminations, II: non-Haken 3-manifolds    J. Amer. Math. Soc., 19 (2006) 625--657 (arXiv:math.GT/0408199)
  12. Compression branched surfaces and tight essential laminations    (preliminary draft, better version coming soon)
  13. On the Heegaard splittings of amalgamated 3-manifolds. Geometry & Topology Monographs , 12 (2007) 157 190
  14. Saddle tangencies and the distance of Heegaard splittings. Albegraic & Geometric Topology , 7 (2007) 1119 1134
  15. Thin position and planar surfaces for graphs in the 3-sphere. Proc. Amer. Math. Soc.138 (2010)  333 340
  16. A quadratic bound on the number of boundary slopes of essential surfaces with bounded genus. (with Ruifeng Qiu and Shicheng Wang). Geom. Dedicata. 147  (2010)   131 138
  17. Heegaard surfaces and the distance of amalgamation. Geometry & Topology 14  (2010), 1871 1919
  18. An algorithm to determine the Heegaard genus of a 3-manifold. Geometry & Topology 15  (2011), 1029 1106 (arXiv:1002.1958)
  19. Images of the disk complex. Geom. Dedicata. 158 (2012) 121 136
  20. Rank and genus of 3-manifolds. J. Amer. Math. Soc. 26 (2013) 777--829. (arXiv:1106.6302)
  21. Small 3-manifolds with large Heegaard distance. Math. Proc. Cambridge Phil. Soc. 155 (2013), 431 – 441 (arXiv:1211.3064)
  22. Taut foliations in knot complements. (with Rachel Roberts) Pacific J. of Math. to appear    (arXiv:1211.3066)
  23. On the degeneration of tunnel numbers under connected sum. (with Ruifeng Qiu)   arXiv: