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Dave Futer: Research

My research is focused on low-dimensional topology and geometry, including the geometry of infinite groups. On a more concrete level, I study knots and links, as well as the 3-dimensional spaces that surround them. I was first drawn to this field by its visual nature and strong geometric flavor. I like seeing things visually, and the pictures of hyperbolic geometry play a significant role in my work. Here is what I do, in a little more detail:


Research papers

The title of the paper links to a PDF. Also, here is a more detailed list, with abstracts.
  1. Essential surfaces in highly twisted link complements.
    With Ryan Blair and Maggy Tomova.
    Algebraic & Geometric Topology 15 (2015) 1501-1523. ArXiv.

  2. Hyperbolic semi-adequate links.
    With Effie Kalfagianni and Jessica Purcell.
    Communications in Analysis & Geometry, to appear. ArXiv.

  3. Quasifuchsian state surfaces.
    With Effie Kalfagianni and Jessica Purcell.
    Transactions of the American Mathematical Society 366 (2014), Issue 8, 4323-4343. ArXiv.

  4. Cusp geometry of fibered 3-manifolds.
    With Saul Schleimer.
    American Journal of Mathematics 136 (2014), Issue 2, 309-356. ArXiv.

  5. Small volume link orbifolds.
    With Chris Atkinson.
    Mathematical Research Letters 20 (2013), Issue 6, 995-1016. ArXiv.

  6. Jones polynomials, volume, and essential knot surfaces: a survey.
    With Effie Kalfagianni and Jessica Purcell.
    Proceedings of Knots in Poland III, Banach Center Publications 100 (2014), Issue 1, 51-77. ArXiv.

  7. Fiber detection for state surfaces.
    Algebraic & Geometric Topology 13 (2013), Issue 5, 2799-2807. ArXiv.

  8. Guts of surfaces and the colored Jones polynomial.
    With Effie Kalfagianni and Jessica Purcell.
    Monograph published in Lecture Notes in Mathematics (Springer), volume 2069 (2013). ArXiv.

  9. Dehn filling and the geometry of unknotting tunnels.
    With Daryl Cooper and Jessica Purcell.
    Geometry & Topology 17 (2013), Issue 3, 1815-1876. ArXiv.

  10. Explicit Dehn filling and Heegaard splittings.
    With Jessica Purcell.
    Communications in Analysis and Geometry 21 (2013), Issue 3, 625-650. ArXiv.

  11. Explicit angle structures for veering triangulations.
    With François Guéritaud.
    Algebraic & Geometric Topology 13 (2013), Issue 1, 205-235. ArXiv.

  12. Surface quotients of hyperbolic buildings.
    With Anne Thomas.
    International Mathematics Research Notices 2012, Issue 2, 437-477. ArXiv.

  13. Volume bounds for generalized twisted torus links.
    With Abhijit Champanerkar, Ilya Kofman, Walter Neumann, and Jessica Purcell.
    Mathematical Research Letters 18 (2011), Issue 6, 1097-1120. ArXiv.

  14. From angled triangulations to hyperbolic structures.
    With François Guéritaud.
    Contemporary Mathematics 541 (2011), 159-182. ArXiv.

  15. Slopes and colored Jones polynomials of adequate knots.
    With Effie Kalfagianni and Jessica Purcell.
    Proceedings of the American Mathematical Society 139 (2011), Issue 5, 1889-1896. ArXiv.

  16. On diagrammatic bounds of knot volumes and spectral invariants.
    With Effie Kalfagianni and Jessica Purcell.
    Geometriae Dedicata 147 (2010), 115-130. ArXiv.

  17. Finite surgeries on three-tangle pretzel knots.
    With Masaharu Ishikawa, Yuichi Kabaya, Thomas Mattman, and Koya Shimokawa.
    Algebraic & Geometric Topology 9 (2009), Issue 2, 743-771. ArXiv.

  18. Cusp areas of Farey manifolds and applications to knot theory.
    With Effie Kalfagianni and Jessica Purcell.
    International Mathematics Research Notices 2010, Issue 23, 4434-4497. ArXiv.

  19. Symmetric links and Conway sums: volume and Jones polynomial.
    With Effie Kalfagianni and Jessica Purcell.
    Mathematical Research Letters 16 (2009), Issue 2, 233-253. ArXiv.

  20. Alternating sum formulae for the determinant and other link invariants.
    With Oliver Dasbach, Effie Kalfagianni, Xiao-Song Lin, and Neal Stoltzfus.
    Journal of Knot Theory and its Ramifications 19 (2010), Issue 6, 765-782. ArXiv.

  21. The Jones polynomial and graphs on surfaces.
    With Oliver Dasbach, Effie Kalfagianni, Xiao-Song Lin, and Neal Stoltzfus.
    Journal of Combinatorial Theory, Series B 98 (2008), Issue 2, 384-399. ArXiv.

  22. Angled decompositions of arborescent link complements.
    With François Guéritaud.
    Proceedings of the London Mathematical Society 98 (2009), Issue 2, 325-364. ArXiv.

  23. Dehn filling, volume, and the Jones polynomial.
    With Effie Kalfagianni and Jessica Purcell.
    Journal of Differential Geometry 78 (2008), Issue 3, 429-464. ArXiv.

  24. Geometric triangulations of two-bridge link complements.
    Appendix to a paper by François Guéritaud.
    Geometry & Topology 10 (2006), 1267-1282. ArXiv.

  25. Links with no exceptional surgeries.
    With Jessica Purcell.
    Commentarii Mathematici Helvetici 82 (2007), Issue 3, 629-664. ArXiv.

  26. Involutions of knots that fix unknotting tunnels.
    Journal of Knot Theory and its Ramifications 16 (2007), Issue 6, 741-748. ArXiv.

  27. Cost-minimizing networks among immiscible fluids in R2.
    With Andrei Gnepp, David McMath, Brian Munson, Ting Fai Ng, Sang-Hyoun Pahk, and Cara Yoder.
    Pacific Journal of Mathematics 196 (2000), Issue 2, 395-414.


Research links

General links:

Visualization software:

  • The KnotPlot Site makes beautiful pictures, including both of the knot pictures on this page.
  • Not Knot, a great visual introduction to hyperbolic geometry
  • Spend an hour or two playing with Jeff Weeks's programs, and you'll understand the idea of a manifold.
  • The program Curved Spaces lets you fly through a 3-manifold and see its intrinsic geometry.
Math research social links:


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dfuter at temple edu
Last modified: Fri Apr 11 11:08:44 PDT 2008