Toric geometry of G2-manifolds

Madsen, Thomas Bruun and Swann, Andrew Toric geometry of G2-manifolds. Geometry & Topology. ISSN 1465-3060 (In Press)

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We consider G2-manifolds with an effective torus action that is multi-Hamiltonian for one or more of the defining forms. The case of T3-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 G2. We prove that the multi-moment 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.

Item Type: Article
Uncontrolled Keywords: g2 manifold, differential geometry, Gibbons–Hawking ansatz
Subjects: Q Science > QA Mathematics
Divisions: School of Science > School of Computing
Depositing User: Thomas Madsen
Date Deposited: 05 Aug 2019 13:50
Last Modified: 05 Aug 2019 13:51

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