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Kael Dixon: Lectures

September 14, 2018
TITLE: Asymptotic properties of toric G2 manifolds

A toric G_2 manifold is a 7-manifold M equipped with a torsion-free G_2 structure, which is invariant under the action of a 3-torus T in such a way that there exist multi-moment maps associated to the G_2 3-form and its Hodge dual. These are introduced and studied in a recent paper by Madsen and Swann, where they show that these multi-moment maps induce a local homeomorphism from the space of orbits M/T into R4. In other words, the multi-moment maps provide geometrically motivated local coordinates for M/T. In all of the known examples, this local homeomorphism is a global homeomorphism onto R4. I will describe some partial results toward showing that this is true in general.

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