Artin辫群子群的拓扑复杂性
Topological complexity of subgroups of Artin's braid groups
摘要：
我们考虑Artin辫子群的子群的拓扑复杂性，该辫子群由辫子组成，其相关排列位于对称群的某个指定子群中。我们给出了这样的混合辫群的拓扑复杂性的上界和下界。特别是，我们表明，任何子群的n-股辫群，固定任何两个股的拓扑复杂性是2n-3，推广的结果Farber和Yuzvinsky在纯辫的情况下。此外，我们推广我们的结果设置更高的拓扑复杂性。
英文摘要：
We consider the topological complexity of subgroups of Artin's braid group consisting of braids whose associated permutations lie in some specified subgroup of the symmetric group. We give upper and lower bounds for the topological complexity of such mixed braid groups. In particular we show that the topological complexity of any subgroup of the n-strand braid group which fixes any two strands is 2n-3, extending a result of Farber and Yuzvinsky in the pure braid case. In addition, we generalise our results to the setting of higher topological complexity.
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