论文标题
具有边界的歧管的点上点式动作
Point-pushing actions for manifolds with boundary
论文作者
论文摘要
给定一个歧管$ m $和内部点的点，点式绘制地图描述了沿封闭路径推动点的差异形态。这将$ m $基本组的同态分别定义为固定底线的$ m $的同位素类别类别。该地图在尺寸上进行了充分研究$ d = 2 $，并且是Birman精确序列的一部分。在这里，我们研究的是，对于任何$ d \ geqslant 3 $和$ k \ geqslant 1 $，从$ k $ th的$ m $组成的地图到$ k $ punctured compunduropt的歧管$ m \ m \ smallepsetminus z $的同型同质式等效的同型同型等价类别的地图。同等地，我们描述了通用捆绑包的单片，该单元将其与配置的$ z $相关联，$ k $ in $ m $，其补充，太空$ m \ smallsetminus z $。此外，由于我们在配置映射空间的同源性的工作中，我们描述了$ m $的编织组对配置映射空间纤维的作用。
Given a manifold $M$ and a point in its interior, the point-pushing map describes a diffeomorphism that pushes the point along a closed path. This defines a homomorphism from the fundamental group of $M$ to the group of isotopy classes of diffeomorphisms of $M$ that fix the basepoint. This map is well-studied in dimension $d = 2$ and is part of the Birman exact sequence. Here we study, for any $d \geqslant 3$ and $k \geqslant 1$, the map from the $k$-th braid group of $M$ to the group of homotopy classes of homotopy equivalences of the $k$-punctured manifold $M \smallsetminus z$, and analyse its injectivity. Equivalently, we describe the monodromy of the universal bundle that associates to a configuration $z$ of size $k$ in $M$ its complement, the space $M \smallsetminus z$. Furthermore, motivated by our work on the homology of configuration-mapping spaces, we describe the action of the braid group of $M$ on the fibres of configuration-mapping spaces.
