论文标题
注入性批次复合的局部结构
The Local Structure of Injective LOT-Complexes
论文作者
论文摘要
标记为定向的树，地段，编码4球中4球中的色带脊柱，并在4个球中2节。这些棘突未解决的非球面问题是怀特海的非球面猜想的主要测试用例。在本文中，我们完整地描述了减少的注射批次复杂的链接。一个重要的情况是：如果$γ$是一个不包含边界减少子点的注入式批次，则$ LK（K（γ））$是双重景点。结果，$ k（γ）$实际上是DR，其基本组在本地表明。我们还表明，一般的注射批次复合物是非球面的。在过去的二十年中，我们的一些结果已经出现在印刷品中，并在此收集。
Labeled oriented trees, LOT's, encode spines of ribbon discs in the 4-ball and ribbon 2-knots in the 4-sphere. The unresolved asphericity question for these spines is a major test case for Whitehead's asphericity conjecture. In this paper we give a complete description of the link of a reduced injective LOT complex. An important case is the following: If $Γ$ is a reduced injective LOT that does not contain boundary reduced sub-LOTs, then $lk(K(Γ))$ is a bi-forest. As a consequence $K(Γ)$ is aspherical, in fact DR, and its fundamental group is locally indicable. We also show that a general injective LOT complex is aspherical. Some of our results have already appeared in print over the last two decades and are collected here.
