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Abstract
We consider G2manifolds with an effective torus action that is multiHamiltonian for one or more of the defining forms. The case of T3actions is found to be distinguished. For such actions multiHamiltonian with respect to both the three and fourform, we derive a GibbonsHawking type ansatz giving the geometry on an open dense set in terms a symmetric 3×3matrix of functions. This leads to particularly simple examples of explicit metrics with holonomy equal to G2. 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 

Publisher  arxiv.org 
Number of pages  33 
Publication status  Published  20 Mar 2018 
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 1 Finished

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