Special holonomy manifolds with torus symmetry

Madsen, Thomas ORCID: https://orcid.org/0000-0001-9354-0935 (2023) Special holonomy manifolds with torus symmetry. NA, London, UK. (Unpublished)

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The focus of this talk will be Calabi-Yau 3-folds and G2
-manifolds. Both types of spaces come with certain geometric data, including a Ricci-flat metric, making it challenging to find explicit examples. A construction by Foscolo-Haskins-Nordstrom provides a way of constructing G2
-manifolds on the total space of a circle bundle over a certain type of Calabi-Yau 3-fold. I will discuss the case where the Calabi-Yau manifold comes equipped with a 3-torus action (partially) preserving the geometric structure. In this instance, we will see that the G2-manifold also admits a 3-torus action and that the orbit space has a natural parameterisation in terms of so-called multi-moment maps. I will also look at the relationship between the combinatorial data of these two types of toric geometries.

Item Type: Other
Keywords: Toric geometry; holonomy; Hamiltonian
Subjects: Mathematics
Depositing User: Thomas Madsen
Date Deposited: 13 Sep 2023 15:13
Last Modified: 13 Sep 2023 15:13
URI: https://repository.uwl.ac.uk/id/eprint/10301

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