Deformation Theory of Asymptotically Conical Coassociative 4-folds

Abstract

We study coassociative 4-folds N in R^7 which are asymptotically conical to a cone C with rate lambda<1. If lambda is in the interval [-2,1) and generic, we show that the moduli space of coassociative deformations of N which are also asymptotically conical to C with rate lambda is a smooth manifold, and we calculate its dimension. If lambda<-2 and generic, we show that the moduli space is locally homeomorphic to the kernel of a smooth map between smooth manifolds, and we give a lower bound for its expected dimension. We also derive a test for when N will be planar if lambda<-2 and we discuss examples of asymptotically conical coassociative 4-folds.

50 pages, LaTeX; v2: numerous presentation improvements and changes, some general theory of elliptic operators between weighted Banach spaces added to aid the reader; v3: further results included and proofs streamlined

References in corpus (3)

• Ruled Lagrangian Submanifolds of the 6-Sphere
• 2-Ruled Calibrated 4-folds in R^7 and R^8
• Coassociative cones that are ruled by 2-planes

Cited by in corpus (8)

• Deformation theory of G_2 conifolds
• Bryant-Salamon ${\mathrm{G}}_2$ manifolds and coassociative fibrations
• Deformations of calibrated subbundles of Euclidean spaces via twisting by special sections
• Asymptotically Conical Associative 3-folds
• Deformations of Asymptotically Conical $G_2$-Instantons
• Manifolds with analytic corners
• Desingularization of Coassociative 4-folds with Conical Singularities: Obstructions and Applications
• Deformations of Compact Coassociative 4-folds with Boundary