On fillings of contact links of quotient singularities

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.

Revised version, dropped the discussion of orbifold fillings with assumptions on orbifold symplectic cohomology, to appear in Journal of Topology

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