Remark on ordered braid groups
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866912450701426688 |
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| author | Nikolaev, Igor |
| author_facet | Nikolaev, Igor |
| contents | We recover the Dehornoy order on the braid group $B_{2g+n}$ from the tracial state on a cluster $C^*$-algebra $\mathbb{A}(S_{g,n})$ associated to the surface $S_{g,n}$ of genus $g$ with $n$ boundary components. It is proved that the space of left-ordering of the fundamental group $π_1(S_{g,n})$ is a totally disconnected dense subspace of the projective Teichmüller space $\mathbb{P}T_{g,n}\cong \mathbf{R}^{6g-7+2n}$. In particular, each left-ordering of $π_1(S_{g,n})$ defines the orbit of a Riemann surface $S_{g,n}$ under the geodesic flow on the space $T_{g,n}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_08103 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Remark on ordered braid groups Nikolaev, Igor Geometric Topology Group Theory Operator Algebras 20F36, 20F60, 46L85 We recover the Dehornoy order on the braid group $B_{2g+n}$ from the tracial state on a cluster $C^*$-algebra $\mathbb{A}(S_{g,n})$ associated to the surface $S_{g,n}$ of genus $g$ with $n$ boundary components. It is proved that the space of left-ordering of the fundamental group $π_1(S_{g,n})$ is a totally disconnected dense subspace of the projective Teichmüller space $\mathbb{P}T_{g,n}\cong \mathbf{R}^{6g-7+2n}$. In particular, each left-ordering of $π_1(S_{g,n})$ defines the orbit of a Riemann surface $S_{g,n}$ under the geodesic flow on the space $T_{g,n}$. |
| title | Remark on ordered braid groups |
| topic | Geometric Topology Group Theory Operator Algebras 20F36, 20F60, 46L85 |
| url | https://arxiv.org/abs/2206.08103 |