# The normal closure of a bounding pair map in its mapping class group

## TL;DR

This paper generalizes Johnson's result by describing the normal subgroup generated by genus n bounding pair maps in the mapping class group using Chillingworth and Casson–Morita invariants.

## Contribution

It provides two new descriptions of the normal subgroup generated by genus n bounding pair maps, extending Johnson's findings to higher genus cases.

## Key findings

- Normal subgroup generated by genus n bounding pair maps characterized.
- Descriptions using Chillingworth and Casson–Morita invariants provided.
- Generalization of Johnson's result to higher genus bounding pairs.

## Abstract

Johnson showed that the normal subgroup of a mapping class group generated by the genus $1$ bounding pair maps is equal to the Torelli group. Generalizing Johnson's result, we give two descriptions of the normal subgroup generated by the genus $n$ bounding pair maps using the Chillingworth and the Casson--Morita invariants.