Notes on hyperbolic knot theory:

I am currently turning some notes on hyperbolic knot theory into a book. Come back soon for more information.

New: Updated drafts of chapters.
Posted here are drafts of some of the current chapters. I'm very interested in feedback from students and other mathematicians.

  1. Introduction [pdf]
  2. Decomposition of the figure-8 knot [pdf]
  3. Calculating in hyperbolic space [pdf]
  4. Geometric structures on manifolds [pdf]
  5. Hyperbolic structures and triangulations [pdf]
  6. Discrete groups and the thick-thin decomposition [pdf]
  7. Completion and Dehn filling [pdf]
  8. Twist knots [pdf]
  9. Essential surfaces [pdf]
  10. Volume and angle structures [pdf]
  11. Two-bridge knots [pdf] (updated September 2017)
  12. Alternating knots [pdf] (updated September 2017)
  13. The geometry of embedded surfaces
  14. Ford domains and canonical polyhedra
  15. Volume
  16. Representations and the A-polynomial
  17. Tunnel number one knots
  18. Bibliography and index [pdf]