b_1=0 的三维流形的 Seiberg-Witten-Floer 稳定同伦型
微分几何
2019-06-25 v5 几何拓扑
摘要
利用 Furuta 在 Seiberg-Witten 理论中有限维逼近的思想，我们细化 Seiberg-Witten Floer 同调，得到一个存在于 S^1-等变分次悬范畴中的同调三维球面的不变量。特别地，这给出了一种避免标准方法中精细横截性问题的 Seiberg-Witten Floer 同调的构造。我们还定义了带边界四维流形的一个相对不变量，它推广了闭四维流形的 Bauer-Furuta 稳定同伦不变量。
引用
@article{arxiv.math/0104024,
title = {Seiberg-Witten-Floer stable homotopy type of three-manifolds with b_1=0},
author = {Ciprian Manolescu},
journal= {arXiv preprint arXiv:math/0104024},
year = {2019}
}
备注
v4, added errata: In Section 9, the Coulomb-Neumann condition should be replaced by a double Coulomb condition, as in Khandhawit's paper (arxiv:1401.7590). Other minor errors are fixed. The main results are unchanged. Version 3 was published in Geom. Topol. 7(2003) 889-932; current version contains appended errata. v5: added item (4) to the errata