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

  1. 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.
  2. Examples of non-trivial roots of unity at ideal points of hyperbolic 3-manifolds. Topology 38 (1999), 457 - 465. math.GT/9801064.
  3. Cyclic surgery, degrees of maps of character curves, and volume rigidity for hyperbolic manifolds. Invent. Math. 136 (1999) 3, 623-657. math.GT/9802022.
  4. A table of boundary slopes of Montesinos knots. Topology, 40 (2001) 2, 309-315. math.GT/9901120. Associated software.
  5. Alexander and Thurston norms of fibered 3-manifolds. Pacific J. Math. 200 (2001), 43-58. math.GT/9908050.
  6. With Danny Calegari. Commensurability of 1-cusped hyperbolic 3-manifolds. Trans. Amer. Math. Soc. 354 (2002), 2921-2932. math.GT/0102024.
  7. With Danny Calegari. Laminations and groups of homeomorphisms of the circle. Invent. Math. 152 (2003) 149-207. math.GT/0203192.
  8. With Bill Thurston. The Virtual Haken Conjecture: Experiments and Examples. Geom. Topol. 7 (2003) 399-441. math.GT/0209214. Associated software and data.
  9. 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.
  10. 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.
  11. 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.
  12. With Bill Thurston. Finite covers of random 3-manifolds. Invent. Math. 166 (2006) 457-521. math.GT/0502567.
  13. With Sergei Gukov and Jake Rasmussen. The superpolynomial for knot homologies. Experimental Math. 15 (2006), 129-159. math.GT/0505662.
  14. 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.
  15. With Frank Calegari. Automorphic forms and rational homology 3-spheres, Geom. Topol. 10 (2006) 295-329. math.GT/0508271. Associated data.
  16. 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.
  17. With S. Garoufalidis, A. Shumakovitch, and M. Thistlethwaite. Behavior of knot invariants under genus 2 mutation. Preprint, 2006. 15 pages. math.GT/0607258.
  18. With Dinakar Ramakrishnan. Increasing the number of fibered faces of arithmetic hyperbolic 3-manifolds. Preprint, 2007. 40 pages. arXiv:0712.3243. Associated software and data.

Slides from talks

  1. Which small volume hyperbolic 3-manifolds are Haken? PDF or PostScript (Warwick, 1999).
  2. Does a random tunnel-number one 3-manifold fiber over the circle? PDF or PostScript (Treiste 2005).
  3. Mathematical Truths: Experiment, Proof, and Understanding. PDF (From a public lecture at Bowdoin Collge in 2007).

Miscellaneous unpublished work

  1. An interesting relationship between the Jones polynomial and hyperbolic volume. Web (2000).

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