Homological stability for quotients of mapping class groups of surfaces by the Johnson subgroups

2017/04/04 by Tomáš Zeman, Zeman, Tomáš
Mathematics · #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1704.01176

openalex publication_date 2017/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study quotients of mapping class groups (Γ_g,1) of oriented surfaces with one boundary component by terms of their Johnson filtrations, and we show that the homology of these quotients with suitable systems of twisted coefficients stabilises as the genus of the surface goes to infinity. We also compute the stable (co)homology with constant rational coefficients for one family of such quotients.

Related

• Improved homological stability for the mapping class group with integral or twisted coefficients
• Surfaces in a background space and the homology of mapping class groups
• Homological stability of non-orientable mapping class groups with marked points
• Stability for closed surfaces in a background space
• The first homology group with twisted coefficients for the mapping class group of a non-orientable surface with boundary