Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2511.00438 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909881704906752 |
|---|---|
| author | Qiu, Yu Zhou, Yu |
| author_facet | Qiu, Yu Zhou, Yu |
| contents | Let $\mathbf{S}$ be a marked surface with vortices (=punctures with extra $\mathbb{Z}_2$ symmetry). We study the decorated version $\mathbf{S}_\bigtriangleup$, where the $\mathbb{Z}_2$ symmetry lifts to the relation that the fourth power of the braid twist of any collision path (connecting a decoration in $\bigtriangleup$ and a vortex) is identity.
We prove the following three groups are isomorphic: King-Qiu's cluster braid group associated to $\mathbf{S}$, the braid twist group of $\mathbf{S}_\bigtriangleup$ and the fundamental group of Bridgeland-Smith's moduli space of $\mathbf{S}$-framed GMN differentials. Moreover, we give finite presentations of such groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_00438 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Decorated Marked Surfaces with vortices: Cluster braid group vs. braid twist group Qiu, Yu Zhou, Yu Representation Theory Geometric Topology Let $\mathbf{S}$ be a marked surface with vortices (=punctures with extra $\mathbb{Z}_2$ symmetry). We study the decorated version $\mathbf{S}_\bigtriangleup$, where the $\mathbb{Z}_2$ symmetry lifts to the relation that the fourth power of the braid twist of any collision path (connecting a decoration in $\bigtriangleup$ and a vortex) is identity. We prove the following three groups are isomorphic: King-Qiu's cluster braid group associated to $\mathbf{S}$, the braid twist group of $\mathbf{S}_\bigtriangleup$ and the fundamental group of Bridgeland-Smith's moduli space of $\mathbf{S}$-framed GMN differentials. Moreover, we give finite presentations of such groups. |
| title | Decorated Marked Surfaces with vortices: Cluster braid group vs. braid twist group |
| topic | Representation Theory Geometric Topology |
| url | https://arxiv.org/abs/2511.00438 |