The article by Swann & Madsen; Toric geometry of G2-manifolds is accepted for publication in Geometry and Topology.

In this article Swann & Madsen 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, they 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. They 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". 

The article was first published on ArXiv.org in March 2018