Hyperbolic 3-manifolds

Math 86500 [ 17462 ] Spring 2012

Thursday, 2 - 4 pm, Room 8405

Instructor: Abhijit Champanerkar
Office: 4214-08
Email :
Office Hours: Thursday 12.30 - 2 pm

Course Outline and Reference Books

Topic-wise suggested reading

1. Basics of 3-manifolds
   • Notes on Geometry and 3-manifolds by Walter Neumann, Chapter 2 (Classical Theory and JSJ Decomposition)


2. Geometrization of 3-manifolds
   • Notes on Geometry and 3-manifolds by Walter Neumann, Chapter 1 (Geometric Structures on 2- and 3-Manifolds)
   • The geometries of 3-manifolds by Peter Scott.
   • Geometric Structures on 3-manifold by Francis Bonahon


3. Hyperbolic plane and Hyperbolic space
   • Chapter 2 (for hyperbolic plane) and Chapter 9 (hyperbolic space) from the book Low-Dimensional Geometry by Francis Bonahon.


4. Margulis Lemma and Mostow Rigidity
   • For details see Chapter C & D from Lectures on Hyperbolic Geometry by Benedetti and Petronio
   • Chapter 6 from Thurston's notes


5. Ideal triangulations & Knot complements
   • For details see Chapter E, Section E.5 & * from Lectures on Hyperbolic Geometry by Benedetti and Petronio
   • Chapter 4 from Thurston's notes
   • Chapter 11 from Low-Dimensional Geometry by Francis Bonahon.


6. Hyperbolic Volume
   • Chapter 7 from Thurston's notes
   • Chapter 10, Section 10.4 from Foundations of Hyperbolic Manifolds by Ratcliffe


7. Computational tools: SnapPea, SnapPy, Snap
   • SnapPea
   • SnapPy
   • Snap
   • Table of Knot Invariants


8. Dehn Surgery Theorem



9. Canonical decompositions, Dirichlet domains etc

Final Project

For the final project students have to write a two page report on a recent paper on hyperbolic 3-manifolds. The report should be written using Latex and submitted as a pdf file by May 25 . Students should meet with the instructor to choose and discuss the paper.

List of papers you can choose from.

Useful Links:

1. CUNY Geometry and Topology Seminar
   Tuesdays 4:10 - 5:10 pm, Room 3212