## Abstract

Stable generalized complex structures can be constructed out of boundary Lefschetz fibrations. On 4-manifolds, these are essentially genus one Lefschetz fibrations over surfaces, except that generic fibres can collapse to circles over a codimension 1 submanifold, which is often the boundary of the surface. We show that a 4-manifold admits a boundary Lefschetz fibration over the disc degenerating over its boundary if and only if it is diffeomorphic to S
^{1}
×S
^{3}
#nℂP
^{2}
, #mℂP
^{2}
#nℂP
^{2}
or #m(S
^{2}
×S
^{2}
).We conclude that the 4-manifolds S
^{1}
×S
^{3}
#nℂP
^{2}
, #(2m+1)ℂP
^{2}
#nℂP
^{2}
and #(2m+1)S
^{2}
×S
^{2}
admit stable generalized complex structures whose type change locus has a single component.

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

Title of host publication | Geometry and Physics |

Subtitle of host publication | A Festschrift in Honour of Nigel Hitchin |

Publisher | Oxford University Press |

Pages | 399-418 |

Number of pages | 20 |

Volume | 2 |

ISBN (Electronic) | 9780198802020 |

DOIs | |

Publication status | Published - 1 Jan 2018 |

## Keywords

- 4-manifold
- Generalized complex structure
- Lefschetz fibration