## Abstract

We construct many new topological types of compact G2-manifolds, that is, Riemannian 7-manifolds with holonomy group G_{2}. To achieve this we extend the twisted connected sum construction first developed by Kovalev and apply it to the large class of asymptotically cylindrical Calabi-Yau 3-folds built from semi-Fano 3-folds constructed previously by the authors. In many cases we determine the diffeomorphism type of the underlying smooth 7-manifolds completely; we find that many 2-connected 7-manifolds can be realized as twisted connected sums in a variety of ways, raising questions about the global structure of the moduli space of G_{2}-metrics. Many of the G_{2}-manifolds we construct contain compact rigid associative 3-folds, which play an important role in the higher-dimensional enumerative geometry (gauge theory/ calibrated submanifolds) approach to defining deformation invariants of G_{2}-metrics. By varying the semi-Fanos used to build different G_{2}-metrics on the same 7-manifold we can change the number of rigid associative 3-folds we produce.

Original language | English |
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Pages (from-to) | 1971-2092 |

Number of pages | 122 |

Journal | Duke Mathematical Journal |

Volume | 164 |

Issue number | 10 |

Early online date | 14 Jul 2015 |

DOIs | |

Publication status | Published - 15 Jul 2015 |

## ASJC Scopus subject areas

- Mathematics(all)

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