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Moduli Spaces of Riemann Surfaces
About this Title
Benson Farb, University of Chicago, Chicago, IL, Richard Hain, Duke University, Durham, NC and Eduard Looijenga, Tsinghua University, Beijing, China, Editors
Publication: IAS/Park City Mathematics Series
Publication Year:
2013; Volume 20
ISBNs: 978-0-8218-9887-1 (print); 978-1-4704-0994-4 (online)
DOI: https://doi.org/10.1090/pcms/020
MathSciNet review: MR3114680
MSC: Primary 14-06; Secondary 14H10, 32-06, 57S05
ReadershipTable of Contents
Front/Back Matter
Chapters
- Introduction
- A brief introduction to mapping class groups
- Teichmüller theory
- The Mumford conjecture, Madsen-Weiss and homological stability for mapping class groups of surfaces
- Lectures on the Madsen-Weiss theorem
- The Torelli group and congruence subgroups of the mapping class group
- Tautological algebras of moduli spaces of curves
- Mirzakhani’s volume recursion and approach for the Witten-Kontsevich theorem on moduli tautological intersection numbers
- Teichmüller curves, mainly from the viewpoint of algebraic geometry
- Introduction to arithmetic mapping class groups