论文标题
迷失方向的同源性和双支封面
Disoriented homology and double branched covers
论文作者
论文摘要
本文提供了一种方便且实用的方法，可以计算4球的分支双层盖的同源性和交点配对。 要投影3球中的链接，以及四球中的表面投影到边界球体中，我们将一系列同源组（称为迷失的同源性）关联。我们表明，迷失的同源性与链接或表面的双支盖的同源性是同构。我们在表面的第一个迷失方向同源组上定义了一个配对，并表明这等于分支盖的相交配对。这些结果将戈登和莉丝兰（Gordon and Litherland）的工作概括为3个球体中的嵌入式表面，并在4球中任意表面。我们还将Gordon-Litherland的签名公式概括为一般环境。 我们的结果是由定理描述了$ n $ ball中Codimension-2 submanifold的分支双重盖的句柄分解的基础，该封面概述了Akbulut-Kirby等的先前结果。
This paper provides a convenient and practical method to compute the homology and intersection pairing of a branched double cover of the 4-ball. To projections of links in the 3-ball, and to projections of surfaces in the 4-ball into the boundary sphere, we associate a sequence of homology groups, called the disoriented homology. We show that the disoriented homology is isomorphic to the homology of the double branched cover of the link or surface. We define a pairing on the first disoriented homology group of a surface and show that this is equal to the intersection pairing of the branched cover. These results generalize work of Gordon and Litherland, for embedded surfaces in the 3-sphere, to arbitrary surfaces in the 4-ball. We also give a generalization of the signature formula of Gordon-Litherland to the general setting. Our results are underpinned by a theorem describing a handle decomposition of the branched double cover of a codimension-2 submanifold in the $n$-ball, which generalizes previous results of Akbulut-Kirby and others.
