一个新的 4 流形不变量。
A new invariant of 4-manifolds.
机构信息
Department of Mathematics, University of California, Berkeley, CA 94720;
Department of Mathematics, University of California, Davis, CA 95616.
出版信息
Proc Natl Acad Sci U S A. 2018 Oct 23;115(43):10857-10860. doi: 10.1073/pnas.1718953115.
Abstract
We define an integer invariant [Formula: see text] of a smooth, compact, closed 4-manifold X by minimizing a certain complexity of a trisection of X over all trisections. The good feature of [Formula: see text] is that when [Formula: see text] and X is a homology 4-sphere, then X is diffeomorphic to the 4-sphere. Naturally, L is hard to compute.
摘要
我们通过在所有三分叉中最小化 X 的三分叉复杂度来定义光滑、紧致、闭 4 流形 X 的整数不变量 [公式：见正文]。[公式：见正文] 的一个很好的特点是，当 [公式：见正文] 且 X 是一个同调 4-球体时，那么 X 与 4-球体同胚。自然地，L 很难计算。
相似文献
1
A new invariant of 4-manifolds.一个新的 4 流形不变量。
Proc Natl Acad Sci U S A. 2018 Oct 23;115(43):10857-10860. doi: 10.1073/pnas.1718953115.
2
Generalized trisections in all dimensions.高维广义三分。
Proc Natl Acad Sci U S A. 2018 Oct 23;115(43):10908-10913. doi: 10.1073/pnas.1718961115.
3
Bridge trisections of knotted surfaces in 4-manifolds.桥截断 4 流形中的纽结曲面。
Proc Natl Acad Sci U S A. 2018 Oct 23;115(43):10880-10886. doi: 10.1073/pnas.1717171115.
4
Calculating the homology and intersection form of a 4-manifold from a trisection diagram.从三分图计算四流形的同调与交形。
Proc Natl Acad Sci U S A. 2018 Oct 23;115(43):10869-10874. doi: 10.1073/pnas.1717176115.
5
Characterizing Dehn surgeries on links via trisections.通过三分(trisections)刻画链的 Dehn 手术。
Proc Natl Acad Sci U S A. 2018 Oct 23;115(43):10887-10893. doi: 10.1073/pnas.1717187115.
6
Computing trisections of 4-manifolds.计算 4 维流形的三分点。
Proc Natl Acad Sci U S A. 2018 Oct 23;115(43):10901-10907. doi: 10.1073/pnas.1717173115.
7
Trisections of 4-manifolds with boundary.带边界的 4 维流形的三分叉。
Proc Natl Acad Sci U S A. 2018 Oct 23;115(43):10861-10868. doi: 10.1073/pnas.1717170115. Epub 2018 Oct 22.
8
Simplified broken Lefschetz fibrations and trisections of 4-manifolds.简化的破裂 Lefschetz 纤维化与 4 维流形的三分叉
Proc Natl Acad Sci U S A. 2018 Oct 23;115(43):10894-10900. doi: 10.1073/pnas.1717175115. Epub 2018 Oct 22.
9
Heegaard Floer homology for manifolds with torus boundary: properties and examples.具有环面边界的流形的希盖尔弗勒同调：性质与示例。
Proc Lond Math Soc. 2022 Oct;125(4):879-967. doi: 10.1112/plms.12473. Epub 2022 Sep 8.
10
Topology of surface diagrams of smooth 4-manifolds.光滑 4 维流形的曲面图的拓扑结构。
Proc Natl Acad Sci U S A. 2011 May 17;108(20):8126-30. doi: 10.1073/pnas.1016952108. Epub 2011 Apr 25.
引用本文的文献
1
Trisections of 4-manifolds.4维流形的三等分
Proc Natl Acad Sci U S A. 2018 Oct 23;115(43):10853-10856. doi: 10.1073/pnas.1717166115.
Zotero 插件