Publications and Preprints
All of my papers and preprints are stored on arXiv.org. Each paper below is
linked to the user-friendly UC Davis Front to the
archive. The papers here are the definitive versions. They are
identical in content to the published versions except where the
journal introduced errors (e.g. the hilarious references to "Inventory
Mathematics" in the published version of paper 2).
Publications and preprints
- With N. Brown and G. Perry. Colorings of the plane. Parts I,
II, and III. Geombinatorics 3 (1993), no. 2,
24-31; 3(1994), no. 3, 64-74; 3 (1994), no. 4,
110-114.
- Examples of non-trivial roots of unity at ideal
points of hyperbolic 3-manifolds. Topology
38 (1999), 457 - 465.
math.GT/9801064.
- Cyclic surgery, degrees of maps of character curves,
and volume rigidity for hyperbolic manifolds.
Invent. Math. 136 (1999) 3, 623-657.
math.GT/9802022.
- A table of boundary slopes of Montesinos knots.
Topology, 40 (2001) 2, 309-315.
math.GT/9901120. Associated software.
- Alexander and Thurston norms of fibered
3-manifolds. Pacific
J. Math. 200 (2001), 43-58.
math.GT/9908050.
- With Danny Calegari. Commensurability of 1-cusped hyperbolic
3-manifolds. Trans. Amer. Math. Soc. 354 (2002), 2921-2932.
math.GT/0102024.
- With Danny Calegari. Laminations and groups of
homeomorphisms of the circle. Invent. Math. 152 (2003) 149-207. math.GT/0203192.
- With Bill Thurston. The Virtual Haken Conjecture:
Experiments and Examples. Geom. Topol. 7
(2003) 399-441. math.GT/0209214.
Associated software and data.
- With Stavros Garoufalidis. Non-triviality of the A-polynomial for knots in the 3-sphere.
Algebr. Geom. Topology 4 (2004), 1145-1153. math.GT/0405353.
- The Mahler measure of the A-polynomial of m129(0,3).
Appendix to D. Boyd and F. Rodriguez Villegas, Mahler's measure and
the dilogarithm (II). math.NT/0308041.
- With Danny Calegari. An ascending HNN extension of a free group inside SL(2,C). Proc. Amer. Math. Soc. 134 (2006) 3131-3136. math.GR/0412136.
- With Bill Thurston. Finite covers of random
3-manifolds. Invent. Math. 166 (2006) 457-521. math.GT/0502567.
- With Sergei Gukov and Jake Rasmussen. The superpolynomial for knot homologies. Experimental Math. 15 (2006), 129-159. math.GT/0505662.
- Volume change under drilling: theory vs. experiment.
Appendix to Agol, Storm, and W. Thurston, Lower bounds on
volumes of hyperbolic Haken 3-manifolds, J. Amer. Math. Soc. 20 (2007), 1053-1077.
math.DG/0506338.
- With Frank Calegari. Automorphic forms and rational
homology 3-spheres, Geom. Topol. 10 (2006) 295-329. math.GT/0508271.
Associated data.
- With Dylan Thurston. A random tunnel number one 3-manifold does not fiber over the circle. Geom. Topol. 10 (2006) 2431-2499. math.GT/051029.
- With S. Garoufalidis, A. Shumakovitch, and M. Thistlethwaite.
Behavior of knot invariants under genus 2 mutation. New York J. Math., 16 (2010) 99-123. math.GT/0607258.
- With Dinakar Ramakrishnan. Increasing the number of
fibered faces of arithmetic hyperbolic 3-manifolds. Amer. J. Math 132 (2010), 53-97. arXiv:0712.3243. Associated software and data.
- With John W. Aaber. Closed surface bundles of least
volume, Algebr. Geom. Topology 10 (2010), 2315-2342. arXiv:1002.3423.
- With Helen Wong. Quantum invariants of random
3-manifolds, Algebr. Geom. Topology 11 (2011) 2191-2205. arXiv:1009.1653.
- With Anil Hirani. The Least Spanning Area of a Knot and
the Optimal Bounding Chain Problem, SoCG 2011: Proceedings of the
27th annual ACM symposium on Computational Geometry, pages 135-144. arXiv:1012.303.
- With Stavros Garoufalidis. Incompressibility criteria for
spun-normal surfaces,
Trans. Amer. Math. Soc. 64 (2012) 6109-6137. arXiv:1102.4588.
- With Stefan Friedl and Nicholas Jackson. Twisted Alexander
polynomials of hyperbolic knots, Experimental
Math., 21 (2012), 329-352. arXiv:1108.3045.
Associated software and data.
- With Jeff Brock. Injectivity radii of hyperbolic integer
homology 3-spheres, to appear in Geom. Topol. 30 pages, arXiv:1304.0391 .
- Which small volume hyperbolic 3-manifolds are Haken?
PDF or PostScript (Warwick, 1999).
- Does a random tunnel-number one 3-manifold fiber over the circle?
PDF or PostScript (Treiste 2005).
- Mathematical Truths: Experiment, Proof, and Understanding.
PDF (From a public lecture at Bowdoin Collge in 2007).
- Surfaces in finite covers of 3-manifolds: the Virtual Haken
Conjecture: PDF (Single), PDF (Double). (Invited address at the AMS meeting in Raleigh, April 2009.)
- Practical solutions to hard problems in 3-dimensional topology: PDF (Single), PDF (Double) (Hamilton Geometry and Topology Workshop, September 2009.)
- Hyperbolically twisted Alexander polynomials of knots: PDF (Single), PDF (Double) (Jacofest, June 2010)
- The Least Spanning Area of a Knot and the Optimal Homologous
Chain Problem: PDF (Single), PDF (Double) (SoCG, Paris, June 2011)
- The Least Spanning Area of a Knot and the Optimal Homologous
Chain Problem: PDF (Single), PDF (Double) (Hyamfest, July 2011)
- Hyperbolically twisted Alexander polynomials of knots
: PDF (Single), PDF (Double). Complete
video. (CBMS-NSF Conference, NYC, August 2011)
- Hyperbolically twisted Alexander polynomials of knots
: PDF (Single), PDF (Double). (Gauge Theory Seminar,
Harvard, April 2012)
- Hyperbolic geometry of integer homology 3-spheres.
Complete
video. (Banff, July 2012)
- Surfaces in finite covers of 3-manifolds: the Virtual Haken
Conjecture Complete
video. (GEAR retreat, Urbana, August 2012)
- L-spaces and left-orderability: an experimental survey.
Complete
video. (Banff, April 2013)
- Integer homology 3-spheres with large injectivity radius.
Complete
video. (GTiNY2013, Columbia University, July 2013)
Miscellaneous unpublished work
- An interesting relationship between the Jones polynomial and hyperbolic
volume. Web (2000).