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T2-invariant associatives in G2 manifolds with cohomogeneity-two symmetry.

Federico Trinca

A classical way to construct calibrated submanifolds is via symmetry reduction. In this talk, we will consider G2 manifolds with a T2 x SU(2) structure-preserving action of cohomogeneity-two. For each of these manifolds, we describe the geometry of the T2-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 S3 x R4. This is joint work in progress with B. Aslan.


Simons- Special Holonomy in Geometry, Analysis, and Physics: Progress and Open Problems