The Torelli group and congruence subgroups of the mapping class group
arXiv:1201.3946 · doi:10.1090/pcms/020
Abstract
These are the lecture notes for my course at the 2011 Park City Mathematics Graduate Summer School. The first two lectures covered the basics of the Torelli group and the Johnson homomorphism, and the third and fourth lectures discussed the second cohomology group of the level p congruence subgroup of the mapping class group, following my papers "The second rational homology group of the moduli space of curves with level structures" and "The Picard group of the moduli space of curves with level structures".
26 pages, 8 figures; to appear in Park City Mathematics Series
References in corpus (8)
- Stabilization for mapping class groups of 3-manifolds
- Homological stability for mapping class groups of surfaces
- The abelianization of the level 2 mapping class group
- Irreducible Sp-representations and subgroup distortion in the mapping class group
- The second rational homology group of the moduli space of curves with level structures
- The Johnson homomorphism and its kernel
- The abelianization of the level L mapping class group
- Generating the Torelli group