论文标题
图形，球形的同拷贝组以及长链接和结的空间
Graphing, homotopy groups of spheres, and spaces of long links and knots
论文作者
论文摘要
我们研究了至少三个欧几里得空间中长连接的空间的同源群。由于多个组件，他们承认从同型球体组中注射分裂。我们表明，在打结之前，这些解释了所有范围内的所有同拷贝组，该范围取决于源歧管和目标歧管的尺寸，并大致概括了同位素类别的三分之三的范围。在此范围之遥之后，连接组件既将参数化的长浮球环类也发送给长结空间的第一个非平凡同型组的发电机。对于大多数源尺寸的等准长链接的空间，我们用这些硼圈环和同型球体组描述了同型组的发电机。在我们大多数结果中，一个关键成分是图形映射，该图将源和目标维度增加一个。
We study homotopy groups of spaces of long links in Euclidean space of codimension at least three. With multiple components, they admit split injections from homotopy groups of spheres. We show that, up to knotting, these account for all the homotopy groups in a range which depends on the dimensions of the source manifolds and target manifold and which roughly generalizes the triple-point-free range for isotopy classes. Just beyond this range, joining components sends both a parametrized long Borromean rings class and a Hopf fibration to a generator of the first nontrivial homotopy group of the space of long knots. For spaces of equidimensional long links of most source dimensions, we describe generators for the homotopy group in this degree in terms of these Borromean rings and homotopy groups of spheres. A key ingredient in most of our results is a graphing map which increases source and target dimensions by one.
