Exotic Stein fillings with arbitrary fundamental group

Anar Akhmedov, Burak Ozbagci

Research output: Contribution to journalArticle

Abstract

Let G be a finitely presentable group. We provide an infinite family of homeomorphic but pairwise non-diffeomorphic, symplectic but non-complex closed 4-manifolds with fundamental group G such that each member of the family admits a Lefschetz fibration of the same genus over the two-sphere. As a corollary, we also show the existence of a contact 3-manifold which admits infinitely many homeomorphic but pairwise non-diffeomorphic Stein fillings such that the fundamental group of each filling is isomorphic to G. Moreover, we observe that the contact 3-manifold above is contactomorphic to the link of some isolated complex surface singularity equipped with its canonical contact structure.

Original languageEnglish (US)
Pages (from-to)265-281
Number of pages17
JournalGeometriae Dedicata
Volume195
Issue number1
DOIs
StatePublished - Aug 1 2018

Keywords

  • Contact structures
  • Exotic manifolds
  • Lefschetz fibrations
  • Stein fillings
  • Symplectic manifolds

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