Notes on hyperbolic knot theory:

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

Updated 29 March, 2018.
Posted here are drafts of some of the current chapters. I'm very interested in feedback from students and other mathematicians.

  1. Preface, Table of Contents (draft) [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 and augmented links [pdf]
  9. Essential surfaces [pdf]
  10. Volume and angle structures [pdf]
  11. Two-bridge knots [pdf]
  12. Alternating knots [pdf]
  13. The geometry of embedded surfaces [pdf]
  14. Volume estimates [pdf]
  15. Ford domains and canonical polyhedra
  16. Representations and the A-polynomial
  17. Tunnel number one knots
  18. Bibliography and index [pdf]