On fillings of contact links of quotient singularities

Pub Date : 2024-03-09 DOI:10.1112/topo.12329

Zhengyi Zhou

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Abstract

We study several aspects of fillings for links of general isolated quotient singularities using Floer theory, including co-fillings, Weinstein fillings, strong fillings, exact fillings and exact orbifold fillings, focusing on the non-existence of exact fillings of contact links of isolated terminal quotient singularities. We provide an extensive list of isolated terminal quotient singularities whose contact links are not exactly fillable, including $C^{n} / (Z / 2)$ for $n ⩾ 3$ , which settles a conjecture of Eliashberg, quotient singularities from general cyclic group actions and finite subgroups of $S U (2)$ , and all terminal quotient singularities in complex dimension 3. We also obtain uniqueness of the orbifold diffeomorphism type of exact orbifold fillings of contact links of some isolated terminal quotient singularities.

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论商数奇点接触链路的填充

我们用弗洛尔理论研究了一般孤立商奇点的链接填充的几个方面，包括共填充、韦恩斯坦填充、强填充、精确填充和精确轨道填充，重点研究了孤立末端商奇点的接触链接不存在精确填充的问题。我们列举了大量接触链接不可精确填充的孤立末端商奇点，其中包括 n ⩾ 3 $n\geqslant 3$ 时的 C n / ( Z / 2 ) ${\mathbb {C}}^n/({\mathbb {Z}}/2)$ 、这解决了埃利亚斯伯格的猜想、来自一般循环群作用和 S U ( 2 ) $SU(2)$的有限子群的商奇异点，以及复维度 3 中的所有末端商奇异点。我们还得到了一些孤立的末端商奇点的接触链接的精确球面填充的球面衍射类型的唯一性。

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