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Abstract
We consider G _{2} –manifolds with an effective torus action that is multiHamiltonian for one or more of the defining forms. The case of T ^{3} –actions is found to be distinguished. For such actions multiHamiltonian with respect to both the threeand fourform, 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 fourmanifold containing a trivalent graph as the image of the set of special orbits and describe these graphs in some complete examples.
Original language  English 

Journal  Geometry & Topology 
Volume  23 
Issue  7 
Pages (fromto)  34593500 
Number of pages  42 
ISSN  14653060 
DOIs  
Publication status  Published  Dec 2019 
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Dive into the research topics of 'Toric geometry of G2manifolds'. Together they form a unique fingerprint.Projects
 1 Finished

Torus symmetry and Einstein metrics
Swann, A. F. (Participant)
Independent Research Fund Denmark
01/11/2016 → 31/12/2019
Project: Research