Aarhus University Seal

Toric geometry of G2-manifolds

Research output: Working paper/Preprint Working paperResearch

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.
Original languageEnglish
Number of pages33
Publication statusPublished - 20 Mar 2018

See relations at Aarhus University Citationformats


ID: 124953039