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)

Preview

Text Spin7toric_accpeted.pdf - Accepted Version Download (308kB) | Preview

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.

Actions (login required)

View Item