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Symplectic fillings of lens spaces as Lefschetz fibrations

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Bhupal, M.

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We construct a positive allowable Lefschetz fibration over the disk on any minimal (weak) symplectic filling of the canonical contact structure on a lens space. Using this construction we prove that any minimal symplectic filling of the canonical contact structure on a lens space is obtained by a sequence of rational blowdowns from the minimal resolution of the corresponding complex two-dimensional cyclic quotient singularity.

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European Mathematical Society

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Mathematics, Applied mathematics

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Journal of The European Mathematical Society

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10.4171/JEMS/621

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