Johnson's homomorphisms and the rational cohomology of subgroups of the mapping class group

Sakasai, Takuya

doi:10.2969/aspm/05210093

VOL. 52 | 2008 Johnson's homomorphisms and the rational cohomology of subgroups of the mapping class group

Chapter Author(s) Takuya Sakasai

Editor(s) Robert Penner, Dieter Kotschick, Takashi Tsuboi, Nariya Kawazumi, Teruaki Kitano, Yoshihiko Mitsumatsu

Adv. Stud. Pure Math., 2008: 93-109 (2008) DOI: 10.2969/aspm/05210093

Abstract

The Torelli group and the Johnson kernel are important subgroups of the mapping class group of a surface. Using Johnson's homomorphisms as their free abelian quotients together with the representation theory of the symplectic groups, we will give some descriptions of cup products of rational cohomology classes of degree one obtained from the dual of Johnson's homomorphisms.