2012/01/18 by Yusuke Kuno, Kuno, Yusuke, Robert Penner +3
Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · doi:10.48550/arxiv.1201.3808
openalex publication_date 2012/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Λ3 K. Furthermore, the Earle class with coefficients in K is represented by an explicit cocyle.