Deformations of conically singular Cayley submanifolds (Q2318025)

A submanifold of a spin\((7)\)-manifold which is calibrated by the Cayley form is called a Cayley submanifold. Examples include complex two-dimensional submanifolds and special Lagrangians in a Calabi-Yau four-fold. In this article, the author studies the deformations of a Cayley submanifold which possesses a conical singularity. The deformations under consideration preserve the singularity. The expected dimension of the moduli space of these deformations turns out to be the index of a certain first-order linear elliptic operator. In case the Cayley-submanifold is a complex two-dimensional submanifold of a Calabi-Yau four-fold, the moduli space is a smooth manifold. The author calculates several examples.