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 (last updated 30 May 2017).
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]
  12. Alternating knots
  13. Ford domains and canonical polyhedra
  14. Volume
  15. Representations and the A-polynomial
  16. Tunnel number one knots
  17. Bibliography and index [pdf]