Graph braid groups and right-angled Artin groups

Graph braid groups and right-angled Artin groups
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图编织组和直角 Artin 组

DOI：
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发表时间：
2008
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影响因子：
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通讯作者：
H. Park
H. Park
中科院分区：
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文献类型：
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作者：
Jee Hyoun Kim;K. Ko;H. Park

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给出了一个图具有直角Artin群作为其辫子群的一个充要条件。为了有必要部分，图被组织成小类，以便可以应用直角Artin群的同调或上同调特征之一。最后，我们证明了一个给定的图是平面图的当且仅当它的2-辫群的第一个同调是无挠的，并且留下关于$n$-辫群的相应陈述作为猜想，以及关于其指标为$le4$的辫群是直角Artin群的图的一些其他猜想。
We give a necessary and sufficient condition for a graph to have a right-angled Artin group as its braid group for braid index $ge 5$. In order to have the necessity part, graphs are organized into small classes so that one of homological or cohomological characteristics of right-angled Artin groups can be applied. Finally we show that a given graph is planar iff the first homology of its 2-braid group is torsion-free and leave the corresponding statement for $n$-braid groups as a conjecture along with few other conjectures about graphs whose braid groups of index $le 4$ are right-angled Artin groups.