4-球面与5-球中的纽结柄体
几何拓扑
2023-07-04 v4
摘要
对每个整数 ，我们构造光滑嵌入于 中的三维亏格- 1-柄体，它们具有相同的边界，且由边界上相同的割系统所定义，然而即使将其内部推入 ，它们也不能通过任何局部平坦同伦在边界相对意义下同伦。这证明了 Budney-Gabai 关于亏格至少为 2 的猜想。
引用
@article{arxiv.2111.13255,
title = {Knotted handlebodies in the 4-sphere and 5-ball},
author = {Mark Hughes and Seungwon Kim and Maggie Miller},
journal= {arXiv preprint arXiv:2111.13255},
year = {2023}
}
备注
11 pages, 3 figures. Various minor changes were made in this version to address referee comments. This version has been accepted for publication in the Journal of the European Mathematical Society