تقرير
Rigidity of braid group actions on $\mathbb{R}$ and of low-genus mapping class group actions on $S^1$
| العنوان: | Rigidity of braid group actions on $\mathbb{R}$ and of low-genus mapping class group actions on $S^1$ |
|---|---|
| المؤلفون: | Ba, Idrissa, Clay, Adam, Ghaswala, Tyrone |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Geometric Topology, 20F60 (Primary) 20F36, 37E05, 37E10, 57K20 (Secondary) |
| الوصف: | Every nontrivial action of the braid group $B_n$ on $\mathbb{R}$ by orientation-preserving homeomorphisms yields, up to conjugation by a homeomorphism of $\mathbb{R}$, a representation $\rho : B_n \rightarrow \mathrm{H\widetilde{ome}o}_+(S^1)$ and therefore determines a translation number for every element of $B_n$. In this manuscript we offer a simple characterisation of which actions of $B_n$ on $\mathbb{R}$ produce translation numbers that agree with those arising from the standard Nielsen-Thurston action on $\mathbb{R}$. Our approach is to prove an analogous statement concerning left orderings of $B_n$ via a technique that uses the space of left orderings of $B_n$, the isolated points in this space, and the natural conjugacy action of $B_n$. We use this result to extend recent rigidity results of Mann and Wolff concerning mapping class group actions on $S^1$ to the case of low-genus surfaces with marked points. Comment: 25 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2312.10727 |
| رقم الأكسشن: | edsarx.2312.10727 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |