### Abstract

Auroux, Donaldson and Katzarkov introduced broken Lefschetz fibrations as a generalization of Lefschetz fibrations in order to describe near-symplectic 4-manifolds. We first study monodromy representations of higher sides of genus-1 simplified broken Lefschetz fibrations. We then completely classify diffeomorphism types of such fibrations with connected fibers and with less than six Lefschetz singularities. In these studies, we obtain several families of genus-1 simplified broken Lefschetz fibrations, which we conjecture contain all such fibrations, and determine the diffeomorphism types of the total spaces of these fibrations. Our results are generalizations of Kas' classification theorem of genus-1 Lefschetz fibrations, which states that the total space of a nontrivial genus-1 Lefschetz fibration over S2 is diffeomorphic to an elliptic surface E.n/ for some n ≤ 1.

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

Pages (from-to) | 1267-1322 |

Number of pages | 56 |

Journal | Algebraic and Geometric Topology |

Volume | 11 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2011 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Geometry and Topology

### Cite this

**On genus-1 simplified broken lefschetz fibrations.** / Hayano, Kenta.

Research output: Contribution to journal › Article

*Algebraic and Geometric Topology*, vol. 11, no. 3, pp. 1267-1322. https://doi.org/10.2140/agt.2011.11.1267

}

TY - JOUR

T1 - On genus-1 simplified broken lefschetz fibrations

AU - Hayano, Kenta

PY - 2011

Y1 - 2011

N2 - Auroux, Donaldson and Katzarkov introduced broken Lefschetz fibrations as a generalization of Lefschetz fibrations in order to describe near-symplectic 4-manifolds. We first study monodromy representations of higher sides of genus-1 simplified broken Lefschetz fibrations. We then completely classify diffeomorphism types of such fibrations with connected fibers and with less than six Lefschetz singularities. In these studies, we obtain several families of genus-1 simplified broken Lefschetz fibrations, which we conjecture contain all such fibrations, and determine the diffeomorphism types of the total spaces of these fibrations. Our results are generalizations of Kas' classification theorem of genus-1 Lefschetz fibrations, which states that the total space of a nontrivial genus-1 Lefschetz fibration over S2 is diffeomorphic to an elliptic surface E.n/ for some n ≤ 1.

AB - Auroux, Donaldson and Katzarkov introduced broken Lefschetz fibrations as a generalization of Lefschetz fibrations in order to describe near-symplectic 4-manifolds. We first study monodromy representations of higher sides of genus-1 simplified broken Lefschetz fibrations. We then completely classify diffeomorphism types of such fibrations with connected fibers and with less than six Lefschetz singularities. In these studies, we obtain several families of genus-1 simplified broken Lefschetz fibrations, which we conjecture contain all such fibrations, and determine the diffeomorphism types of the total spaces of these fibrations. Our results are generalizations of Kas' classification theorem of genus-1 Lefschetz fibrations, which states that the total space of a nontrivial genus-1 Lefschetz fibration over S2 is diffeomorphic to an elliptic surface E.n/ for some n ≤ 1.

UR - http://www.scopus.com/inward/record.url?scp=79960704066&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79960704066&partnerID=8YFLogxK

U2 - 10.2140/agt.2011.11.1267

DO - 10.2140/agt.2011.11.1267

M3 - Article

VL - 11

SP - 1267

EP - 1322

JO - Algebraic and Geometric Topology

JF - Algebraic and Geometric Topology

SN - 1472-2747

IS - 3

ER -