Models for configuration space in a simplicial complex
Models for configuration space in a simplicial complex
复制标题
单纯复形中的配置空间模型
DOI：
10.4064/cm7331-5-2018
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发表时间：
2017
影响因子：
0.4
通讯作者：
John D. Wiltshire
中科院分区：
文献类型：
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作者：
John D. Wiltshire
我们生产的组合模型的配置空间在一个单纯的复杂，并为配置附近的一个单一的点（“本地配置空间。“）局部位形空间的模型是由有限集合上的偏序集结构的偏序集建立的。全局配置空间的模型依赖于一个组合模型与删除subcomplex单纯复杂。作为应用，我们研究了节曲线y^2 z = x^3 + x^2 z$，得到了它的两股辫群的表示，三股辫群的几何表示，以及它的两股和三股局部辫群在奇点附近的表示.
We produce combinatorial models for configuration space in a simplicial complex, and for configurations near a single point ("local configuration space.") The model for local configuration space is built out of the poset of poset structures on a finite set. The model for global configuration space relies on a combinatorial model for a simplicial complex with a deleted subcomplex. By way of application, we study the nodal curve $y^2 z = x^3 + x^2 z$, obtaining a presentation for its two-strand braid group, a conjectural presentation for its three-strand braid group, and presentations for its two- and three-strand local braid groups near the singular point.