Madsen, Thomas Bruun and Swann, Andrew (2019) Toric geometry of G2manifolds. Geometry & Topology, 23 (7). pp. 34593500. ISSN 14653060

Text
Toric Geometry Madsen.pdf Download (391kB)  Preview 
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.
Item Type:  Article 

Uncontrolled Keywords:  g2 manifold, differential geometry, Gibbons–Hawking ansatz 
Subjects:  Q Science > QA Mathematics 
Divisions:  School of Computing 
Depositing User:  Thomas Madsen 
Date Deposited:  05 Aug 2019 13:50 
Last Modified:  10 Feb 2020 16:27 
URI:  http://bear.buckingham.ac.uk/id/eprint/366 
Actions (login required)
View Item 