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Geometriae Dedicata

, Volume 195, Issue 1, pp 265–281 | Cite as

Exotic Stein fillings with arbitrary fundamental group

  • Anar Akhmedov
  • Burak OzbagciEmail author
Original Paper

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.

Keywords

Lefschetz fibrations Stein fillings Contact structures Exotic manifolds Symplectic manifolds 

Mathematics Subject Classification (2000)

57R17 

Notes

Acknowledgements

The authors would like to thank the anonymous referee for his careful reading of the manuscript and his/her suggestions that improved the presentation greatly. The authors would also like to thank R. İ. Baykur for helpful comments.

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Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.School of MathematicsUniversity of MinnesotaMinneapolisUSA
  2. 2.Department of MathematicsUCLALos AngelesUSA
  3. 3.Department of MathematicsKoç UniversityIstanbulTurkey

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