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Abstract
We consider G 2 –manifolds with an effective torus action that is multi-Hamiltonian for one or more of the defining forms. The case of T 3 –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 G 2 . We prove that the multimoment 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.
Originalsprog | Engelsk |
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Tidsskrift | Geometry & Topology |
Vol/bind | 23 |
Nummer | 7 |
Sider (fra-til) | 3459-3500 |
Antal sider | 42 |
ISSN | 1465-3060 |
DOI | |
Status | Udgivet - dec. 2019 |
Fingeraftryk
Dyk ned i forskningsemnerne om 'Toric geometry of G2-manifolds'. Sammen danner de et unikt fingeraftryk.Projekter
- 1 Afsluttet
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Torus symmetry and Einstein metrics
Swann, A. F. (Deltager)
01/11/2016 → 31/12/2019
Projekter: Projekt › Forskning