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Noncomplex smooth 4-manifolds with genus-2 Lefschetz fibrations |
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| Authors: | Burak Ozbagci Andrá s I Stipsicz |
| Institution: | Department of Mathematics, University of California Irvine, Irvine, California 92697 ; Department of Analysis, ELTE TTK, Múzeum krt. 6-8, Budapest, Hungary |
| Abstract: | We construct noncomplex smooth 4-manifolds which admit genus-2 Lefschetz fibrations over |
| Keywords: | Lefschetz fibrations 4-manifolds complex structures |
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. The fibrations are necessarily hyperelliptic, and the resulting 4-manifolds are not even homotopy equivalent to complex surfaces. Furthermore, these examples show that fiber sums of holomorphic Lefschetz fibrations do not necessarily admit complex structures.