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arXiv · 2208.06086

On fillings of contact links of quotient singularities

Zhengyi Zhou
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Abstract

We study several aspects of fillings for links of general quotient singularities using Floer theory, including co-fillings, Weinstein fillings, strong fillings, exact fillings and exact orbifold fillings, focusing on 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 $\mathbb{C}^n/(\mathbb{Z}/2)$ for $n\ge 3$, which settles a conjecture of Eliashberg, quotient singularities from general cyclic group actions and finite subgroups of $SU(2)$, 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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Zhengyi Zhou. 2022-08-12. On fillings of contact links of quotient singularities. https://doi.org/10.1112/topo.12329

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