论文标题
末端的极端非唯一性
Extreme Nonuniqueness of End-Sum
论文作者
论文摘要
我们给出了一对单一开放的4个manifolds对的明确示例，其末端午间会产生许多具有不同合适类型的多种歧管。这在Siebenmann的肯定猜想中对终端和终点的非唯一性有很大的肯定回答。除了构建这些示例之外，我们还提供了用于区分它们的工具的详细讨论；最重要的是，终端循环学代数。我们主要定理的关键是了解该代数的终端和汇总代数，以及由用于执行末端和末端的射线确定的射线 - 汇号类别。不同的射线基础类使我们能够区分各种示例，但仅通过无限产生的阿贝尔群体的微妙理论。包括附录，其中包含来自该区域的必要背景。
We give explicit examples of pairs of one-ended, open 4-manifolds whose end-sums yield uncountably many manifolds with distinct proper homotopy types. This answers strongly in the affirmative a conjecture of Siebenmann regarding the nonuniqueness of end-sums. In addition to the construction of these examples, we provide a detailed discussion of the tools used to distinguish them; most importantly, the end-cohomology algebra. Key to our Main Theorem is an understanding of this algebra for an end-sum in terms of the algebras of the summands together with ray-fundamental classes determined by the rays used to perform the end-sum. Differing ray-fundamental classes allow us to distinguish the various examples, but only through the subtle theory of infinitely generated abelian groups. An appendix is included which contains the necessary background from that area.
