in Functional Analysis, Geometry

Deformation theory of Cayley submanifolds

I just published my first paper on the arxive here. It’s about the deformation theory of conically singular and asymptotically conical Cayley manifolds, based on the work of McLean and Moore. I prove the usual theorems about the existence of Kuranishi charts and discuss some relations to lower-dimensional geometries, such as special Lagrangian, complex and coassociative geometries. For example, special Lagrangians in Calabi-Yau fourfolds will always be obstructed as Cayleys. It is the first in a series of three papers working towards constructing fibrations of compact Spin(7) manifolds by Cayley submanifolds. The next paper which is about the desingularisation of Cayley submanifolds will follow shortly.