Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.14616 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908662711189504 |
|---|---|
| author | Chen, Lei Chen, Weiyan |
| author_facet | Chen, Lei Chen, Weiyan |
| contents | Justin Lanier and the authors recently determined the group normally generated by a single bounding pair map of genus $n$. We related this subgroup with the Chillingworth subgroup and the Casson--Morita's $d$ map. In this paper, we extend the results to the case when $n=0$. Let $\mathcal{M}_g^1$ be the mapping class group, $\text{Ch}_g^1$ be the Chillingworth subgroup and $d$ be the Casson--Morita's $d$-map. We show that $\text{Ker}(d)=[\text{Ch}_g^1,\mathcal{M}_g^1]$ and it is generated by a single homological genus 0 bounding pair map. We also construct an element $H_0\in \text{Ch}_g^1$, and show that $\text{Ch}_g^1$ is normally generated by this single element $H_0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_14616 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The normal closure of a homological genus 0 bounding pair map Chen, Lei Chen, Weiyan Geometric Topology Justin Lanier and the authors recently determined the group normally generated by a single bounding pair map of genus $n$. We related this subgroup with the Chillingworth subgroup and the Casson--Morita's $d$ map. In this paper, we extend the results to the case when $n=0$. Let $\mathcal{M}_g^1$ be the mapping class group, $\text{Ch}_g^1$ be the Chillingworth subgroup and $d$ be the Casson--Morita's $d$-map. We show that $\text{Ker}(d)=[\text{Ch}_g^1,\mathcal{M}_g^1]$ and it is generated by a single homological genus 0 bounding pair map. We also construct an element $H_0\in \text{Ch}_g^1$, and show that $\text{Ch}_g^1$ is normally generated by this single element $H_0$. |
| title | The normal closure of a homological genus 0 bounding pair map |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2511.14616 |