Abstract:

Vector cross products (VCPs) are known to be closely related to calibrated geometry. In particular, certain calibrated submanifolds can be viewed as images of VCP preserving maps. In this talk, we will be interested in the class of "conformally VCP preserving maps" (originally introduced by A. Smith under a different name), which may be thought of as weakly conformal parametrizations of associative (Cayley, resp.) objects in a - (Spin(7)-, resp.) manifold. Our main result is a bubble tree convergence theorem for a sequence of conformally VCP preserving maps with uniformly bounded energy. This is joint work with S. Karigiannis (Waterloo) and J. Madnick (McMaster).