发表机构
Vrije Universiteit Amsterdam（阿姆斯特丹自由大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出三维球体的混合构型空间，证明其到圆构型空间的投影为局部平凡纤维化，并利用不动点的Nielsen等价刻画环辫的共轭关系，推广了二维辫群结果。
AI 中文摘要
我们引入了三维球体混合构型空间的概念。即，我们同时考虑三维球体内部的不同圆和不同点，并证明了到三维球体圆构型空间的投影是一个局部平凡纤维化。定义混合构型空间的关键思想是研究三维球体的保定向同胚的不动点，这些同胚保持三维球体内部由n个分量组成的平凡链环不变。特别地，我们证明了两个不动点是Nielsen等价的，当且仅当相关的环辫被秩为n的某个显著自由子群的一个元素共轭。这一结果作为二维结果的3维对应，其中带孔圆盘同胚的不动点通过经典Artin辫群的辫元来刻画。
英文摘要
We introduce the notion of mixed configuration spaces of the $3$-ball. That is, we consider both distinct circles and distinct points in the interior of the $3$-ball and we prove that the projection onto the configuration space of circles of the $3$-ball is a locally trivial fibration. The key idea for defining the mixed configuration spaces is to study fixed points of orientation-preserving homeomorphism of the $3$-ball that leave invariant a trivial link of $n$ components in the interior of the $3$-ball. In particular, we prove that two fixed points are Nielsen equivalent if and only if the associated loop braids are conjugate by an element of a distinguished free subgroup of rank $n$. This result stands as a $3$-dimensional counterpart of the $2$-dimensional result where fixed points of homeomorphisms of the punctured disc are characterized in terms of braid elements of the classical Artin braid group.
Comments17 pages, 1 figure
