Publications
- Immersed essential surfaces in hyperbolic 3-manifolds. Comm. Anal. Geom. 10 (2002), 275--290.
- Boundary curves of surfaces with 4-plane property. Geometry & Topology, 6 (2002), 609--647.
- Laminar branched surfaces in 3-manifolds. Geometry & Topology, 6 (2002), 153--194.
- Commutator groups and foliations without holonomy. Proc. Amer. Math. Soc. 130 (2002), 2471--2477.
- Boundary train tracks of laminar branched surfaces Proc. of Symposia in Pure Math., 71, AMS (2003), 269--285.
- An algorithm to detect laminar 3-manifolds. (with Ian Agol) Geometry & Topology, 7 (2003), 287--309.
- Property P for knots admitting certain Gabai disks. (with Oliver Dasbach) Topology and its Applications, 142, (2004) 113--129.
- The Waldhausen conjecture (a 4-page outline of the proof of the Waldhausen conjecture) Oberwolfach Report 2005.
- An algorithm to find vertical tori in small Seifert fiber spaces. Commertarii Mathematici Helvetici, 81 (2006) 727--753.
- Heegaard surfaces and measured laminations, I: the Waldhausen conjecture Invent. Math. 167 (2007) 135 – 177 (arXiv:math.GT/0408198)
- Heegaard surfaces and measured laminations, II: non-Haken 3-manifolds J. Amer. Math. Soc., 19 (2006) 625--657 (arXiv:math.GT/0408199)
- Compression branched surfaces and tight essential laminations (preliminary draft, better version coming soon)
- On the Heegaard splittings of amalgamated 3-manifolds. Geometry & Topology Monographs , 12 (2007) 157 – 190
- Saddle tangencies and the distance of Heegaard splittings. Albegraic & Geometric Topology , 7 (2007) 1119 – 1134
- Thin position and planar surfaces for graphs in the 3-sphere. Proc. Amer. Math. Soc.138 (2010) 333 – 340
- 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
- Heegaard surfaces and the distance of amalgamation. Geometry & Topology 14 (2010), 1871 – 1919
- An algorithm to determine the Heegaard genus of a 3-manifold. Geometry & Topology 15 (2011), 1029 – 1106 (arXiv:1002.1958)
- Images of the disk complex. Geom. Dedicata. 158 (2012) 121 – 136
- Rank and genus of 3-manifolds. J. Amer. Math. Soc. 26 (2013) 777--829. (arXiv:1106.6302)
- Small 3-manifolds with large Heegaard distance. Math. Proc. Cambridge Phil. Soc. 155 (2013), 431 – 441 (arXiv:1211.3064)
- Taut foliations in knot complements. (with Rachel Roberts) Pacific J. of Math. 269 (2014), 149 – 168 (arXiv:1211.3066)
- On the degeneration of tunnel numbers under connected sum. (Joint with Ruifeng Qiu) Trans. Amer. Math. Soc. 368 (2016), 2793 – 2807
