New series in the Johnson cokernels of the mapping class groups of surfaces

2010/12/10 by Naoya Enomoto, Enomoto, Naoya, Takao Satoh +1 · 4 citations
Mathematics · #20G05 (primary) #57M99 (secondary) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1012.2175

openalex publication_date 2010/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the present paper, we study the Sp-module structure of the cokernel of the Johnson homomorphism of the mapping class groups of surfaces. We detect the Sp-irreducible components with highest weight [1^k] (and [k]) in the cokernel. We also show that the multiplicities of them is equal to one.

Cited by

• Uniqueness of the non-commutative divergence cocycle
• On the 2-loop part of the Johnson cokernel
• One-dimensionality of certain cocycles for the detection of the Johnson cokernel
• Intersections of curves on surfaces and their applications to mapping class groups

Related

• Marked fatgraph complexes and surface automorphisms
• Homological stability for quotients of mapping class groups of surfaces by the Johnson subgroups
• On the 2-loop part of the Johnson cokernel
• Cup products in surface bundles, higher Johnson invariants, and MMM classes
• A solvable extended logarithm of the Johnson homomorphism