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.
Bibliographical noteFunding Information:
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. ?. Baykur for helpful comments. 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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- Contact structures
- Exotic manifolds
- Lefschetz fibrations
- Stein fillings
- Symplectic manifolds