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