Toric geometry of G2-manifolds

TY - UNPB

T1 - Toric geometry of G2-manifolds

AU - Madsen, Thomas Bruun

AU - Swann, Andrew Francis

PY - 2018/3/20

Y1 - 2018/3/20

N2 - We consider G2-manifolds with an effective torus action that is multi-Hamiltonian for one or more of the defining forms. The case of T3-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 G2. We prove that the multi-moment 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.

AB - We consider G2-manifolds with an effective torus action that is multi-Hamiltonian for one or more of the defining forms. The case of T3-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 G2. We prove that the multi-moment 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.

M3 - Working paper

BT - Toric geometry of G2-manifolds

PB - arxiv.org

ER -