Preface
Benson Farb, Richard Hain, and Eduard Looijenga Introduction
Yair N.Minsky
A Brief Introduction to Mapping Class Groups
1. Definitions, examples, basic structure
2. Hyperbolic geometry, laminations and foliations
3. The Nielsen-Thurston classification theorem
4. Classification continued, and consequences
5. Further reading and current events
Bibliography
Ursula Hamenstadt
Teichmuller Theory
Introduction
Lecture 1. Hyperbolic surfaces
Lecture 2. Quasiconformal maps
Lecture 3. Complex structures, Jacobians and the Weil Petersson form
Lecture 4. The curve graph and the augmented Teichmüller space
Lecture 5. Geometry and dynamics of moduli space
Bibliography
Nathalie Wahl The Mumford Conjecture, Madsen-Weiss and Homological Stability for Mapping Class Groups of Surfaces
Introduction
Lecture 1. The Mumford conjecture and the Madsen-Weiss theorem
1. The Mumford conjecture
2. Moduli space, mapping class groups and diffeomorphism groups
3. The Mumford-Morita-Miller classes
4. Homological stability
5. The Madsen-Weiss theorem
6. Exercises
Lecture 2. Homological stability: geometric ingredients
1. General strategy of proof
2. The case of the mapping class group of surfaces
3. The ordered arc complex
4. Curve complexes and disc spaces
5. Exercises
Lecture 3. Homological stability: the spectral sequence argument
1. Double complexes associated to actions on simplicial complexes
2. The spectral sequence associated to the horizontal filtration
3. The spectral sequence associated to the vertical filtration
4. The proof of stability for surfaces with boundaries
5. Closing the boundaries
6. Exercises
Lecture 4. Homological stability: the connectivity argument
1. Strategy for computing the connectivity of the ordered arc complex
2. Contractibility of the full arc complex
3. Deducing connectivity of smaller complexes
4. Exercises
Bibliography
Soren Galatius
Lectures on the Madsen–Weiss Theorem
Lecture 1. Spaces of submanifolds and the Madsen-Weiss Theorem
