Deformation Theory of Asymptotically Conical Coassociative 4-folds

Details Deformation Theory of Asymptotically Conical Coassociative 4-folds Deformation Theory of Asymptotically Conical Coassociative 4-folds

2004-11-05

arxiv.org/abs/math/0411116v3

Proceedings of the London Mathematical Society 99 (2009), 386-424.

Mathematics

Differential Geometry

50 pages, LaTeX; v2: numerous presentation improvements and changes, some general theory of elliptic operators between weighte

Scientific paper

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.

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