构造界定有理同调4-球的有理同调3-球面
几何拓扑
2025-11-26 v3
摘要
我们提出了三大类新的 plumbing 3-流形例子，它们界定有理同调4-球。这些例子利用本文定义的两个操作构造，这两个操作保持不存在阻碍界定有理同调球的格嵌入 obstruction。除本文所示情形外，这些操作在一般情况下是否为有理同调协边仍属开放问题。新例子族包含环面结上大量有理 surgery 的族，我们明确描述了目前已知哪些正环面结拥有界定有理同调球的 surgery。虽非本文重点，我们隐式地确认了针对树状结（arborescent knots）中新的、更复杂的例子（包括许多 Montesinos 结）的 slice-ribbon 猜想。
引用
@article{arxiv.2208.14850,
title = {Constructing Rational Homology 3-Spheres That Bound Rational Homology 4-Balls},
author = {Lisa Lokteva},
journal= {arXiv preprint arXiv:2208.14850},
year = {2025}
}
备注
39 pages, 35 figures. v3: The proof of the three families bounding rational homology balls was wrong in the first version, and restored only for two of the families in the second version. This version contains proofs for all three families. Moreover, this version has been updated for presentation