Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2511.14616 |
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Inhaltsangabe:
- 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 $H_0$.