基于割补拓扑的 Bott-Taubes-Vassiliev 上同调类
几何拓扑
2021-06-23 v5 代数拓扑
摘要
Bott 和 Taubes 利用构型空间上的积分给出了有限型（即 Vassiliev）纽结不变量。随后 Cattaneo、Cotta-Ramusino 和 Longoni 将这些方法与图上同调结合，在高维欧几里得空间中纽结空间的实上同调中构造了“Vassiliev 类”，正如 Kontsevich 最初所设想的。本文中，我们在维数大于三的欧几里得空间中纽结与链环的空间里构造整数值上同调类。对于任意整数值图上闭链，我们通过粘合紧化构型空间的方法构造这样的类。我们的类在先前发现的实上同调类中构成了整数格。因此我们从三价图上闭链获得了非平凡类。我们的方法推广到由模 p 图上闭链产生模 p 类，这些类不必是整数上类的约化。
引用
@article{arxiv.1512.06654,
title = {Bott-Taubes-Vassiliev cohomology classes by cut-and-paste topology},
author = {Robin Koytcheff},
journal= {arXiv preprint arXiv:1512.06654},
year = {2021}
}
备注
Most significant revisions from v4: corrected Main Theorem statement by an integer factor; expanded material on pushforward and its relation to fiber integration for glued manifolds; replaced cellular treatment of fundamental class by homological treatment; and added material on blowups, neatness, and mutual transversality. 48 pages, 4+ figures. Accepted for publication in Internat. J. Math