Symplectic fillings of lens spaces as Lefschetz fibrations


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BHUPAL M. L. , ÖZBAĞCI B.

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, vol.18, no.7, pp.1515-1535, 2016 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 18 Issue: 7
  • Publication Date: 2016
  • Doi Number: 10.4171/jems/621
  • Journal Name: JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.1515-1535
  • Keywords: Symplectic fillings, lens spaces, canonical contact structure, Lefschetz fibrations, RATIONAL BLOWDOWNS, OPEN BOOKS, SINGULARITIES, SURFACE

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.