Deformation of singular fibers of genus two fibrations and small exotic symplectic 4 -manifolds

Anar Akhmedov, Sümeyra Sakalll

Research output: Contribution to journalArticle

Abstract

We introduce the 2-nodal spherical deformation of certain singular fibers of genus two fibrations, and use such deformations to construct various examples of simply connected minimal symplectic 4-manifolds with small topology. More specifically, we construct new exotic minimal symplectic 4-manifolds homeomorphic but not diffeomorphic to ℂℙ 2 #6ℂℙ 2 , ℂℙ 2 #7ℂℙ 2 , and 3ℂℙ 2 #kℂℙ 2 for k = 16, 17, 18, 19 using combinations of such deformations, symplectic blowups, and (generalized) rational blowdown surgery. We also discuss generalizing our constructions to higher genus fibrations using g-nodal spherical deformations of certain singular fibers of genus g ≥ 3 fibrations.

Original languageEnglish (US)
Article number1950017
JournalInternational Journal of Mathematics
Volume30
Issue number3
DOIs
StatePublished - Mar 1 2019

Keywords

  • Lefschetz fibration
  • Symplectic 4-manifold
  • genus two fibration
  • mapping class group
  • rational blowdown

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