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

## TL;DR

This paper investigates the homological stability of quotients of mapping class groups of surfaces by Johnson subgroups, demonstrating stabilization of their homology with twisted coefficients and computing stable (co)homology with rational coefficients.

## Contribution

It establishes homological stability for these quotients and provides explicit calculations of their stable (co)homology with rational coefficients.

## Key findings

- Homology stabilizes as genus increases
- Stable (co)homology computed with rational coefficients
- Results apply to quotients by Johnson filtrations

## Abstract

We study quotients of mapping class groups (\Gamma_{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.