Exotic Stein fillings with arbitrary fundamental group |
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Authors: | Anar Akhmedov Burak Ozbagci |
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Institution: | 1.School of Mathematics,University of Minnesota,Minneapolis,USA;2.Department of Mathematics,UCLA,Los Angeles,USA;3.Department of Mathematics,Ko? University,Istanbul,Turkey |
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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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