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## Abstract

We consider G
_{2} –manifolds with an effective torus action that is multi-Hamiltonian for one or more of the defining forms. The case of T
^{3} –actions is found to be distinguished. For such actions multi-Hamiltonian with respect to both the three-and four-form, we derive a Gibbons–Hawking type ansatz giving the geometry on an open dense set in terms a symmetric 3 ☓ 3 matrix of functions. This leads to particularly simple examples of explicit metrics with holonomy equal to G
_{2} . We prove that the multimoment maps exhibit the full orbit space topologically as a smooth four-manifold containing a trivalent graph as the image of the set of special orbits and describe these graphs in some complete examples.

Original language | English |
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Journal | Geometry & Topology |

Volume | 23 |

Issue | 7 |

Pages (from-to) | 3459-3500 |

Number of pages | 42 |

ISSN | 1465-3060 |

DOIs | |

Publication status | Published - Dec 2019 |

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Dive into the research topics of 'Toric geometry of G2-manifolds'. Together they form a unique fingerprint.## Projects

- 1 Finished