Toric geometry of Spin(7)-manifolds

Thomas, Madsen and Swann, Andrew Toric geometry of Spin(7)-manifolds. International Mathematics Research Notices. ISSN 1073-7928 (In Press)

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Abstract

We study Spin(7)-manifolds with an effective multi-Hamiltonian action of a four-torus. On an open dense set, we provide a Gibbons-Hawking type ansatz that describes such geometries in terms of a symmetric 4×4-matrix of functions. This description leads to the first known Spin(7)-manifolds with a rank 4 symmetry group and full holonomy. We also show that the multi-moment map exhibits the full orbit space topologically as a smooth four-manifold, containing a trivalent graph in R4 as the image of the set of the special orbits.

Item Type: Article
Uncontrolled Keywords: Spin(7)-manifolds
Subjects: Q Science > QA Mathematics
Divisions: School of Computing
Depositing User: Thomas Madsen
Date Deposited: 31 Oct 2019 14:36
Last Modified: 31 Oct 2019 14:36
URI: http://bear.buckingham.ac.uk/id/eprint/409

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