Stein域中的全纯曲线与tau不变量
几何拓扑
2025-11-19 v5 辛几何
摘要
本文的范围有三方面。首先，我们基于Hayden近期的工作，在计算Hedden的tau不变量时，考虑为有理同调球上的Stein可填充接触结构、且为作为伪全纯曲线边界出现的横截链环的情形。这给出了Stein域相对Thom猜想的一个新证明。其次，我们将不变量与Grigsby-Ruberman-Strle拓扑tau不变量进行比较，后者联系于接触结构的结构，从而得到链环类型容许全纯可填充横截代表的拓扑阻碍。最后，我们利用主要结果结合格上同调方法计算透镜空间中某些链环的不变量，并估计其PL切片亏格。
引用
@article{arxiv.2310.08657,
title = {Holomorphic curves in Stein domains and the tau-invariant},
author = {Antonio Alfieri and Alberto Cavallo},
journal= {arXiv preprint arXiv:2310.08657},
year = {2025}
}
备注
In the previous version we sketched a proof of a conjecture of Gompf. This was based on the wrongly deduced Corollary 4.1; that was never used in the paper otherwise, and we saw it as an interesting byproduct of our results. Consequently, the conjecture cannot be approached simply with the methods of this paper. The authors plan to return to this point in a separate manuscript