Department of Mathematics, University of Georgia, Athens, GA 30602;
Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE 68588.
Proc Natl Acad Sci U S A. 2018 Oct 23;115(43):10887-10893. doi: 10.1073/pnas.1717187115.
We summarize and expand known connections between the study of Dehn surgery on links and the study of trisections of closed, smooth 4-manifolds. In particular, we propose a program in which trisections could be used to disprove the generalized property R conjecture, including a process that converts the potential counterexamples of Gompf, Scharlemann, and Thompson into genus four trisections of the standard 4-sphere that are unlikely to be standard. We also give an analog of the Casson-Gordon rectangle condition for trisections that obstructs reducibility of a given trisection.
我们总结并扩展了链接的 Dehn Surgery 研究与封闭、光滑 4 流形的三分研究之间已知的联系。特别是，我们提出了一个方案，其中三分可以用来否定广义性质 R 猜想，包括一个将 Gompf、Scharlemann 和 Thompson 的潜在反例转换为标准 4-球的四分中的反例的过程，这些反例不太可能是标准的。我们还为三分给出了一个类似于 Casson-Gordon 矩形条件的例子，该条件阻碍了给定三分的可约性。
