Mapping Class Group Seminar

Reading List: (subject to change)

A Primer on Mapping Class Groups (Farb, Margalit)

Summary: The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many important theorems, examples, and techniques as possible, quickly and directly, while at the same time giving full details and keeping the text nearly self-contained.

SURFACE GROUPS AND 3-MANIFOLDS WHICH FIBER OVER THE CIRCLE (Thurston)

Summary: The main result (0.1) of this paper is that every atoroidal three-manifold that fibers over the circle has a hyperbolic structure. Consequently, every fibered three-manifold admits a geometric decomposition. The main tool for constructing hyperbolic structures on fibered three-manifolds is the double limit theorem (4.1), which is of interest for its own sake and lays out general conditions under which sequences of quasi-Fuchsian groups have algebraically convergent subsequences.

Semester Schedule:

1/29 Chapter 1: Curves, Surfaces, and Hyperbolic Geometry - Cas

2/5 Chapter 2: Mapping Class Group Basics - Hunter (+Speaker's Notes)

2/12 Chapter 3: Dehn Twists - Charlie

2/19 Chapter 4 + (1/2)5: Generating the Mapping Class Group + Presentations - Luis

2/26 [Seminar Cancelled]

3/5 Exercise Session

3/12 Chapter 7: Torsion - Florian

3/26 Chapter 8: The Dehn-Nielsen-Baer Theorem - Neža

4/2 Chapter 9: Braid Groups - Hannah

4/9 Big Mapping Class Groups - Kai

4/16 Thurston: "Every atoroidal 3-manifold that fibers over the circle is hyperbolic" Part I - Max*