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Federico Trinca: Lectures

September 12, 2022
TITLE: T^2-invariant associatives in G_2 manifolds with cohomogeneity-two symmetry

ABSTRACT: A classical way to construct calibrated submanifolds is via symmetry reduction. In this talk, we will consider G_2 manifolds with a T^2\times SU(2) structure-preserving action of cohomogeneity-two. For each of these manifolds, we describe the geometry of the T^2-invariant associative submanifolds using moment type maps for the group action. As an application, we describe an associative fibration, in the Karigiannis–Lotay sense, on the Bryant–Salamon manifolds S^3\times \mathbb{R}^4.
This is joint work in progress with B. Aslan.