### Abstract

We construct noncomplex smooth 4-manifolds which admit genus-2 Lefschetz fibrations over S^{2}. 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.

Original language | English |
---|---|

Pages (from-to) | 3125-3128 |

Number of pages | 4 |

Journal | Proceedings of the American Mathematical Society |

Volume | 128 |

Issue number | 10 |

Publication status | Published - 2000 |

### Fingerprint

### Keywords

- 4-manifolds
- Complex structures
- Lefschetz fibrations

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Proceedings of the American Mathematical Society*,

*128*(10), 3125-3128.

**Noncomplex smooth 4-manifolds with genus-2 lefschetz fibrations.** / Ozbagci, Burak; Stipsicz, A.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 128, no. 10, pp. 3125-3128.

}

TY - JOUR

T1 - Noncomplex smooth 4-manifolds with genus-2 lefschetz fibrations

AU - Ozbagci, Burak

AU - Stipsicz, A.

PY - 2000

Y1 - 2000

N2 - We construct noncomplex smooth 4-manifolds which admit genus-2 Lefschetz fibrations over S2. 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.

AB - We construct noncomplex smooth 4-manifolds which admit genus-2 Lefschetz fibrations over S2. 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.

KW - 4-manifolds

KW - Complex structures

KW - Lefschetz fibrations

UR - http://www.scopus.com/inward/record.url?scp=23044523357&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=23044523357&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:23044523357

VL - 128

SP - 3125

EP - 3128

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 10

ER -