Symplectic fillings of lens spaces as Lefschetz fibrations

  • Mohan Bhupal

    Middle East Technical University, Ankara, Turkey
  • Burak Ozbagci

    Koç University, Istanbul, Turkey

Abstract

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.

Cite this article

Mohan Bhupal, Burak Ozbagci, Symplectic fillings of lens spaces as Lefschetz fibrations. J. Eur. Math. Soc. 18 (2016), no. 7, pp. 1515–1535

DOI 10.4171/JEMS/621