论文标题
经典结组的环境分类空间
The ambient classifying space of a classical knot group
论文作者
论文摘要
对于一个主要的结组，子午线产生的子群体的分类空间可以看作是结的环境流形的抽象类似物。该环境分类空间的明确模型被构建为结节上的三个球形分支的分支覆盖空间。研究了更通用的分支覆盖空间，并研究了通过有限索引正常子组对环境分类空间的评估。建立了所述空间的各种同源特性，其中一些具有代数数理论的相似之处。特别是，主要结组是Bieri-Eckmann，但不是Poincaré，Bredon cromology在子午线家族方面的双重性小组。
For a prime knot group, the classifying space for the family of the subgroups generated by the meridians can be seen as an abstract analogue of the ambient manifold in which the knot lives. An explicit model of this ambient classifying space is constructed as a branched covering space of the 3-sphere branched over the knot; more general branched covering spaces, obtained quotienting the ambient classifying space by finite-index normal subgroups, are studied. Various homological properties of said spaces are established, some of which have parallels in algebraic number theory. In particular, prime knot groups are shown to be Bieri-Eckmann, but not Poincaré, duality groups for Bredon cohomology with respect to the family of the meridians.
