Marked fatgraph complexes and surface automorphisms

Abstract

Combinatorial aspects of the Torelli-Johnson-Morita theory of surface automorphisms are extended to certain subgroups of the mapping class groups. These subgroups are defined relative to a specified homomorphism from the fundamental group of the surface onto an arbitrary group $K$. For $K$ abelian, there is a combinatorial theory akin to the classical case, for example, providing an explicit cocycle representing the first Johnson homomophism with target ${\Lambda }^{3}K$. Furthermore, the Earle class with coefficients in $K$ is represented by an explicit cocyle.

References in corpus (1)

• Cohomological Aspects of Magnus Expansions