Hierarchies and the curve complex,
Term I, 2010-2011

Course Description

This course will be an elementary introduction the complex of curves of a surface. Following Masur and Minsky's second paper on this topic we will discuss geodesics in the curve complex, the bounded geodesic image theorem, and hierarchies. Along the way we will touch on the marking graph and distance estimates for the mapping class group.

Reviewing the material from the previous two courses (here and here) will be useful but is not a prerequisite.


The schedule has a list of topics, organized by week, and the lecture notes. As the course progresses I will add the lecture notes and other relevant information to this webpage. The schedule is subject to change as needful.

Instructor and Marker

Name Building/Office E-mail Phone Office Hours
Saul Schleimer 35/B2.14 s.schleimer at warwick dot ac dot uk 024 7652 3560 See here.
Jessica Banks N/A jessica.banks at lincoln dot ox dot ac dot uk N/A N/A

Class meetings

Activity Led by Time Building/Room
Lecture Schleimer Tues 12:00-13:00 35/B0.15a
Lecture Schleimer Thur 12:00-13:00 35/B0.15a

Please do ask questions in class. I am also happy to answer questions via email or in office hours.

Assessed work

Marks possible for the course are Distinction, Pass, and Fail. Please email one exercise per week to the marker, cc'ed to the instructor. Include, in all work turned in, your name, the date, and the statement of the exercise.

Reference materials

As the course progresses I hope to revise my Notes on the complex of curves. However, students are advised to read some of the primary material:

  • Curves on 2-manifolds and isotopies, by Epstein.
  • Boundary structure of the modular group, by Harvey.
  • Geometry of the complex of curves II, by Masur and Minsky.

Other works of interest:

  • Conway's ZIP proof of the classification of surfaces, by Francis and Weeks.
  • A primer on mapping class groups, by Farb and Margalit.
  • Knots and links, by Rolfsen.
  • Braids, links, and mapping class groups, by Birman.
  • The geometries of 3-manifolds, by Scott.
  • A representation of orientable combinatorial 3-manifolds, by Lickorish.
  • A finite set of generators for the homeotopy group of a 2-manifold, by Lickorish.
  • On the geometry and dynamics of diffeomorphisms of surfaces, by Thurston.
  • Automorphisms of surfaces after Nielsen and Thurston, by Casson and Bleiler.
  • Knots, links, braids and 3-manifolds, by Prasolov and Sossinsky.
  • Three-dimensional geometry and topology, by Thurston and edited by Levy.
  • Automorphism of complexes of curves and of Teichmuller spaces, by Ivanov.
  • Automorphisms of complexes of curves on punctured spheres and on punctured tori, by Korkmaz.
  • Automorphisms of the complex of curves, by Luo.
  • Hyperbolic groups, by Gromov.
  • The geometry of cycles in the Cayley diagram of a group, by Gilman.
  • On the definition of word hyperbolic groups, by Gilman.
  • Geometry of the complex of curves I, by Masur and Minsky.
  • Intersection numbers and the hyperbolicity of the curve complex, by Bowditch.


Please tell me in person, or via email, about any errors on this website or made in class. I am especially keen to hear about mathematical errors, gaffes, or typos appearing in my notes on the curve complex.