^{1} Department of Mathematics - Centre for Quantum Geometry of Moduli Spaces, Department of Mathematics, Science and Technology, Aarhus University^{2} Tsuda College, Department of Mathematics, Kodaira^{3} Department of Mathematics, Indiana University^{4} Department of Mathematics - Centre for Quantum Geometry of Moduli Spaces, Department of Mathematics, Science and Technology, Aarhus University

DOI:

10.1007/s10711-012-9807-0

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.

Type:

Journal article

Language:

English

Published in:

Geometriae Dedicata, 2013, Vol 167, Issue 1, p. 151-166