pre-prints (linked to the arXiv)
(with Stefan Friedl and Wolfgang Lück)
Groups and polytopes (arXiv), to appear in Proceedings of the Georgia Topology Conference.
- • (with Jonathan Spreer)
The trisection genus of standard simply connected PL 4-manifolds (arXiv),
to appear in SoCG'18: Proceedings of the 34th International Symposium on Computational Geometry.
- • (with Stefan Friedl)
Two-generator one-relator groups and marked polytopes (arXiv), to appear in Annales d'Institut Fourier.
(with Hyam Rubinstein)
Generalised trisections in all dimensions (preprint), to appear in Proceedings of the National Academy of Sciences of the United States of America.
(with Robert C. Haraway III)
Tessellating the moduli space of strictly convex projective structures on the once-punctured torus
(publisher, arXiv), to appear in Experimental Mathematics.
(with Stefan Friedl and Montek Gill)
Linear representations of 3-manifold groups over rings (arXiv), to appear in Proceedings of the American Mathematical Society.
- • (with Jonathan Spreer),
Unravelling the Dodecahedral Spaces (arXiv), to appear in the 2016 MATRIX Annals.
refereed publications in journals or conference proceedings
(with Daryl Cooper and
Deforming convex projective manifolds
(publisher, arXiv), Geometry & Topology 22 (2018) 1349-1404.
(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.
(with Stefan Friedl and Kevin Schreve)
Thurston norm via Fox calculus (arXiv), Geometry & Topology 21 (2017), no. 6, 3759-3784.
(with Feng Luo)
A new combinatorial class of 3-manifold triangulations (arXiv, publisher), Asian Journal of Mathematics 21 (2017), no.3, 543-570.
(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.
- (with Ben Klaff)
A birationality result for character varieties (arXiv, publisher), Mathematical Research Letters 23 (2016), no.4, 1099-1110.
- (with Bus Jaco,
and Jonathan Spreer),
Bounds for the genus of a normal surface (arXiv, publisher), Geometry & Topology 20 (2016) 1625–1671.
(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.
(with Ben Burton,
Murray Elder and
2-manifold recognition is in logspace (arXiv, publisher), Journal of Computational Geometry 7 (2016), no.1, 70-85.
(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).
- (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).
- (with Hyam Rubinstein)
Even triangulations of n-dimensional pseudo-manifolds (arXiv, publisher), Algebraic and Geometric Topology 15 (2015), no. 5, 2949–2984.
- (with Daryl Cooper and
On Convex Projective Manifolds and Cusps (arXiv), Advances in Mathematics 277 (2015), 181-251.
- (with Ben Burton and
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.
- (with Bus Jaco and Hyam Rubinstein)
Z2-Thurston Norm and Complexity of 3-Manifolds (arXiv), Mathematische Annalen 356 (2013) no. 1, 1-22.
- (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.
Degenerations of ideal hyperbolic triangulations (arXiv), Mathematische Zeitschrift 272 (2012), no. 3-4, 793-823.
- (with Ben Burton and Hyam
The Weber-Seifert dodecahedral space is non-Haken (arXiv, publisher), Transactions of the American Mathematical Society 364 (2012), no. 2, 911-932.
- (with Craig Hodgson, Hyam Rubinstein and Henry Segerman)
Veering triangulations admit strict angle structures (arXiv), Geometry & Topology 15 (2011) 2073-2089.
- (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.
- (with Bus Jaco and Hyam Rubinstein)
Coverings and Minimal Triangulations of 3-Manifolds (arXiv), Algebraic and Geometric Topology 11 (2011) 1257-1265.
- (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.
- (with Daryl Cooper)
Thurston norm via normal surfaces (arXiv), Pacific Journal of Mathematics 239 (2009) 1-15.
Normal surfaces in topologically finite 3-manifolds (arXiv), L'Enseignement Mathématique, 54 (2008) 329-380.
- (with Feng Luo and Saul Schleimer)
Geodesic ideal triangulations exist virtually (arXiv), Proceedings of the American Mathematical Society 136 (2008) 2625-2630.
- (with Feng Luo)
Angle structures and normal surfaces (arXiv), Transactions of the American Mathematical Society 360 (2008) 2849-2866.
Not all boundary slopes are strongly detected by the character variety (arXiv), Communications in Analysis and Geometry 15 (2007) 695-723.
Boundary slopes and the logarithmic limit set (arXiv) the paper (minus the example) appeared in Topology 44 (2005) 203-216.
Character varieties of mutative 3-manifolds (arXiv), Algebraic and Geometric Topology 4 (2004) 133-149.
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
- • Structure of 0–efficient or minimal triangulations (publisher), Oberwolfach Reports 9 (2012), no. 2, 1474-1478.
- • Applications of tropical geometry to groups and manifolds (publisher), Oberwolfach Reports 4 (2007), no. 4, 3281-3283.
extended abstracts in conference proceedings
(with Ben Burton, Arne Hillebrand, Maarten Löffler, Saul Schleimer, Dylan Thurston and Wouter van Toll)
On the Topology of Walkable Environments, paper #66 in
EuroCG 2018 European Workshop on Computational Geometry.
survey or expository papers
- • Warum glücklich statt einfach nur normal? (publisher), Mitteilungen der DMV 24 (2016), no. 4, 197–207.
- (with Benjamin Burton, Herbert Edelsbrunner and Jeff Erickson)
Computational Geometric and Algebraic Topology.
Abstracts from the workshop held October 11–17, 2015. Oberwolfach Reports 12 (2015), no. 4, 2637-2699.
Computational & Algorithmic Topology in Sydney,
Gazette of the Australian Mathematical Society, Volume 41, Number 4 (2014) 229-230.
Geometry & Topology Down Under,
Gazette of the Australian Mathematical Society, Volume 38, Number 5 (2011) 261-263.
reviews (linked to zbMath)
Neil R. Hoffman and Jessica S. Purcell: Geometry of planar surfaces and exceptional fillings.
Bull. Lond. Math. Soc. 49, No. 2, 185-201 (2017).
Joshua A. Howie: A characterisation of alternating knot exteriors.
Geom. Topol. 21, No. 4, 2353-2371 (2017).
Daryl Cooper and William Goldman: A 3-manifold with no real projective structure.
Ann. Fac. Sci. Toulouse, Math. (6) 24, No. 5, 1219-1238 (2015).
reviews (linked to MathSciNet; subscription only)
David Gabai, Robert Meyerhoff and Peter Milley: Minimum volume cusped hyperbolic three-manifolds. J. Amer. Math. Soc. 22 (2009), no. 4, 1157--1215.
MR2423275 Bernard Perron: Filtration de Johnson et groupe de Torelli modulo $p$, $p$ premier. (French). C. R. Math. Acad. Sci. Paris 346 (2008), no. 11-12, 667--670.
- MR2390346 Steven Boyer, Marc Culler, Peter Shalen and Xingru Zhang: Characteristic subsurfaces, character varieties and Dehn fillings. Geom. Topol. 12 (2008), no. 1, 233--297.
Hitoshi Murakami: The colored Jones polynomials and the Alexander
polynomial of the figure-eight knot. JP J. Geom. Topol. 7
(2007), no. 2, 249--269.
Kazuhiro Hikami: Asymptotics of the colored Jones polynomial and the A-polynomial. Nuclear Phys. B 773 (2007), no. 3, 184--202.
Hitoshi Murakami: A version of the volume conjecture. Adv. Math. 211 (2007), no. 2, 678--683.
- MR2263219 Ian Agol, Marc Culler and Peter Shalen: Dehn surgery, homology and hyperbolic volume. Algebr. Geom. Topol. 6 (2006), 2297--2312.
- MR2263219 Stefan Friedl and Taehee Kim: The Thurston norm, fibered manifolds and twisted Alexander polynomials. Topology 45 (2006), no. 6, 929--953.
- MR2243744 Jean-Baptiste Meilhan: Goussarov-Habiro theory for string links and the Milnor-Johnson correspondence. Topology Appl. 153 (2006), no. 14, 2709--2729.
- MR2191691 Ser Peow Tan, Yan Loi Wong and Ying Zhang: The SL(2,C) character variety of a one-holed torus. Electron. Res. Announc. Amer. Math. Soc. 11 (2005), 103--110 (electronic).
- MR2199344 Dmitriy Derevnin, Alexander Mednykh and Michele Mulazzani: Volumes for twist link cone-manifolds. Bol. Soc. Mat. Mexicana (3) 10 (2004), Special Issue, 129--145.
- MR2187606 Sam Nelson: Virtual crossing realization. J. Knot Theory Ramifications 14 (2005), no. 7, 931--951.
- MR2153977 Shelly Harvey: Higher-order polynomial invariants of 3-manifolds giving lower bounds for the Thurston norm. Topology 44 (2005), no. 5, 895--945.
- MR2161256 Xingru Zhang: Trace fields of representations and virtually Haken 3-manifolds. Q. J. Math. 56 (2005), no. 3, 431--442.
- MR2135546 Emmanuel Auclair and Christine Lescop: Clover calculus for homology 3-spheres via basic algebraic topology. Algebr. Geom. Topol. 5 (2005), 71--106 (electronic).
- MR2147736 Atsushi Ishii and Taizo Kanenobu: Different links with the same Links-Gould invariant. Osaka J. Math. 42 (2005), no. 2, 273--290.
- MR2116925 Nafaa Chbili: Symétries en dimension trois: une approche quantique. Cubo 6 (2004), no. 4, 133--165.