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.
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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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The first author was partially supported by the NSF Grant DMS-1005741. The second author was partially supported by a BIDEP-2219 research grant of the Scientific and Technological Research Council of Turkey.
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Akhmedov, A., Ozbagci, B. Exotic Stein fillings with arbitrary fundamental group. Geom Dedicata 195, 265–281 (2018). https://doi.org/10.1007/s10711-017-0289-y
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DOI: https://doi.org/10.1007/s10711-017-0289-y