pre-prints (linked to the arXiv)

in press

books

  1. (with Olivier Collin, Stefan Friedl, Cameron Gordon and Liam Watson, eds.) Characters in low-dimensional topology (publisher), Contemporary Mathematics, 760, Centre de Recherches Mathématiques Proceedings. American Mathematical Society, Providence, RI, 2020.
  2. (with Alex Casella and Dominic Tate) Moduli spaces of real projective structures on surfaces (publisher), MSJ Memoirs, 38. Mathematical Society of Japan, Tokyo, 2020. A shorter version is available at the arXiv.
  3. (with Craig Hodgson, Bus Jaco and Marty Scharlemann, eds.) Geometry and Topology Down Under (publisher), Contemp. Math., 597, Amer. Math. Soc., Providence, RI, 2013.

refereed publications in journals or conference proceedings

  1. Tropical varieties associated to ideal triangulations: The Whitehead link complement (publisher, arXiv), 293-339, Contemp. Math., 760, Amer. Math. Soc., Providence, RI, 2020
  2. (with Hyam Rubinstein) Multisections of piecewise linear manifolds (publisher, arXiv), Indiana University Mathematics Journal 69 (2020), 2209-2239
  3. (with Stefan Friedl) Two-generator one-relator groups and marked polytopes (publisher, arXiv), Annales de l'Institut Fourier, (Grenoble) 70 (2020), no. 2, 831-880.
  4. (with Bus Jaco and Hyam Rubinstein and Jonathan Spreer) Z2-Thurston Norm and Complexity of 3-Manifolds, II (publisher, arXiv), Algebraic & Geometric Topology 20-1 (2020), 503-529.
  5. (with Alex Casella and Charlie Katerba) Ideal points of character varieties, algebraic non-integral representations, and undetected closed essential surfaces in 3-manifolds (publisher, arXiv), Proceedings of the American Mathematical Society 148 (2020), no. 5, 2257-2271.
  6. (with Bus Jaco and Hyam Rubinstein and Jonathan Spreer) On minimal ideal triangulations of cusped hyperbolic 3-manifolds (arXiv, publisher), Journal of Topology 13 (2020), no. 1, 308-342.
  7. (with Hyam Rubinstein and Henry Segerman) Traversing three-manifold triangulations and spines (publisher, arXiv), L'Enseignement Mathématique (2) 65 (2019), 155-206.
  8. (with Michelle Chu) Reflections on trisection genus (arXiv, publisher), Revue Roumaine de Mathématiques Pures et Appliquées 64 (2019), 4, 395-402 (Proceedings of JARCS 2017).
  9. (with Stefan Friedl and Wolfgang Lück) Groups and polytopes (arXiv), Breadth in contemporary topology, 57-77, Proc. Sympos. Pure Math., 102, Amer. Math. Soc., Providence, RI, 2019.
  10. (with Robert C. Haraway III) Tessellating the moduli space of strictly convex projective structures on the once-punctured torus (publisher, arXiv), Experimental Mathematics 28 (2019), no. 3, 369-384.
  11. (with Mark Bell, Joel Hass, and Hyam Rubinstein) Computing trisections of 4-manifolds (publisher, arXiv), Proceedings of the National Academy of Sciences of the United States of America, October 23, 2018, 115 (43) 10901-10907.
  12. (with Hyam Rubinstein) Generalised trisections in all dimensions (publisher, preprint), Proceedings of the National Academy of Sciences of the United States of America, October 23, 2018, 115 (43) 10908-10913.
  13. (with Stefan Friedl and Montek Gill) Linear representations of 3-manifold groups over rings (publisher, arXiv), Proceedings of the American Mathematical Society 146 (2018), no. 11, 4951-4966.
  14. (with Jonathan Spreer) The trisection genus of standard simply connected PL 4-manifolds (publisher, arXiv), 34nd International Symposium on Computational Geometry (SoCG 2018). In Leibniz International Proceedings in Informatics (LIPICS), vol. 99, pg. 71:1-71:13, 2018.
  15. (with Jonathan Spreer), Unravelling the Dodecahedral Spaces (publisher, arXiv). In: Wood D., de Gier J., Praeger C., Tao T. (eds) 2016 MATRIX Annals, 323–347, MATRIX Book Series, vol 1., Springer, Cham, 2018.
  16. (with Daryl Cooper and Darren Long) Deforming convex projective manifolds (publisher, arXiv), Geometry & Topology 22 (2018) 1349-1404.
  17. (with Hsien-Chih Chang, Jeff Erickson, David Letscher, Arnaud de Mesmay, Saul Schleimer, Eric Sedgwick, Dylan Thurston) Tightening Curves on Surfaces via Local Moves (publisher), SODA 2018 Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, ACM, 2018, 121-135.
  18. (with Stefan Friedl and Kevin Schreve) Thurston norm via Fox calculus (arXiv), Geometry & Topology 21 (2017), no. 6, 3759-3784.
  19. (with Feng Luo) A new combinatorial class of 3-manifold triangulations (arXiv, publisher), Asian Journal of Mathematics 21 (2017), no.3, 543-570.
  20. (with Alex Casella and Feng Luo) Pseudo-developing maps for ideal triangulations II: Positively oriented ideal triangulations of cone-manifolds (arXiv), Proceedings of the American Mathematical Society 145 (2017), 3543-3560.
  21. (with Ben Klaff) A birationality result for character varieties (arXiv, publisher), Mathematical Research Letters 23 (2016), no.4, 1099-1110.
  22. (with Bus Jaco, Jesse Johnson and Jonathan Spreer), Bounds for the genus of a normal surface (arXiv, publisher), Geometry & Topology 20 (2016) 1625–1671.
  23. (with Sampson Wong) An algorithm for the Euclidean cell decomposition of a cusped strictly convex projective surface (arXiv, publisher), Journal of Computational Geometry 7 (2016), no.1, 237–255.
  24. (with Ben Burton, Murray Elder and Arkadius Kalka) 2-manifold recognition is in logspace (arXiv, publisher), Journal of Computational Geometry 7 (2016), no.1, 70-85.
  25. (with Craig Hodgson, Hyam Rubinstein and Henry Segerman) Triangulations of 3-manifolds with essential edges (arXiv, publisher), Annales de la Faculté des Sciences de Toulouse 24 (2015), no.5, 1103-1145 (special issue dedicated to Michel Boileau).
  26. (with Daryl Cooper) Complexity functions on 1-dimensional cohomology (arXiv, publisher), Revue Roumaine de Mathématiques Pures et Appliquées 60 (2015), no. 4, 535-550 (Proceedings of JARCS 2013).
  27. (with Hyam Rubinstein) Even triangulations of n-dimensional pseudo-manifolds (arXiv, publisher), Algebraic and Geometric Topology 15 (2015), no. 5, 2949–2984.
  28. (with Daryl Cooper and Darren Long) On Convex Projective Manifolds and Cusps (arXiv), Advances in Mathematics 277 (2015), 181-251.
  29. (with Ben Burton and Alexander Coward) Computing closed essential surfaces in knot complements (arXiv, publisher), SoCG '13: Proceedings of the Twenty-Ninth Annual Symposium on Computational Geometry, ACM, 2013, 405-414.
  30. (with Bus Jaco and Hyam Rubinstein) Z2-Thurston Norm and Complexity of 3-Manifolds (arXiv), Mathematische Annalen 356 (2013) no. 1, 1-22.
  31. (with Feng Luo and Tian Yang) Thurston's Spinning Construction and Solutions to the Hyperbolic Gluing Equations for Closed Hyperbolic 3-Manifolds (arXiv), Proceedings of the American Mathematical Society 141 (2013), no. 1, 335-350.
  32. Degenerations of ideal hyperbolic triangulations (arXiv), Mathematische Zeitschrift 272 (2012), no. 3-4, 793-823.
  33. (with Ben Burton and Hyam Rubinstein) The Weber-Seifert dodecahedral space is non-Haken (arXiv, publisher), Transactions of the American Mathematical Society 364 (2012), no. 2, 911-932.
  34. (with Craig Hodgson, Hyam Rubinstein and Henry Segerman) Veering triangulations admit strict angle structures (arXiv), Geometry & Topology 15 (2011) 2073-2089.
  35. (with Henry Segerman) Pseudo-developing maps for ideal triangulations I: Essential edges and generalised hyperbolic gluing equations (arXiv), in Topology and geometry in dimension three, 85-102, Contemp. Math., 560, Amer. Math. Soc., Providence, RI, 2011.
  36. (with Bus Jaco and Hyam Rubinstein) Coverings and Minimal Triangulations of 3-Manifolds (arXiv), Algebraic and Geometric Topology 11 (2011) 1257-1265.
  37. (with Bus Jaco and Hyam Rubinstein) Minimal triangulations for an infinite family of lens spaces (arXiv), Journal of Topology 2 (2009), no. 1, 157-180.
  38. (with Daryl Cooper) Thurston norm via normal surfaces (arXiv), Pacific Journal of Mathematics 239 (2009) 1-15.
  39. Normal surfaces in topologically finite 3-manifolds (arXiv), L'Enseignement Mathématique, 54 (2008) 329-380.
  40. (with Feng Luo and Saul Schleimer) Geodesic ideal triangulations exist virtually (arXiv), Proceedings of the American Mathematical Society 136 (2008) 2625-2630.
  41. (with Feng Luo) Angle structures and normal surfaces (arXiv), Transactions of the American Mathematical Society 360 (2008) 2849-2866.
  42. (with Eric Chesebro) Not all boundary slopes are strongly detected by the character variety (arXiv), Communications in Analysis and Geometry 15 (2007) 695-723.
  43. Boundary slopes and the logarithmic limit set (arXiv) the paper (minus the example) appeared in Topology 44 (2005) 203-216.
  44. Character varieties of mutative 3-manifolds (arXiv), Algebraic and Geometric Topology 4 (2004) 133-149.
  45. On the Kinoshita-Terasaka knot and generalised Conway mutation (223 KB), Journal of Knot Theory and its Ramifications 9 (2000) 557-575.

non-refereed contributions to conference proceedings

extended abstracts in conference proceedings

survey or expository papers

conference reports

course notes

thesis

reviews (linked to zbMath)

reviews (linked to MathSciNet; subscription only)