Desingularization of Coassociative 4-folds with Conical Singularities

Details Desingularization of Coassociative 4-folds with Conical Singularities Desingularization of Coassociative 4-folds with Conical Singularities

2006-11-07

arxiv.org/abs/math/0611183v2

Geometric and Functional Analysis 18 (2008), 2055-2100.

Mathematics

Differential Geometry

50 pages, LaTeX, v2: significant revision of the argument leading to the key Sobolev embedding estimates; additional hypothese

Scientific paper

Given a coassociative 4-fold N with a conical singularity in a varphi-closed 7-manifold M (a manifold endowed with a distinguished closed 3-form varphi), we construct a smooth family, {N'(t): t\in(0,tau)} for some tau>0, of (smooth, nonsingular,) compact coassociative 4-folds in M which converge to N in the sense of currents, in geometric measure theory, as t tends to 0. This realisation of desingularizations of N is achieved by gluing in an asymptotically conical coassociative 4-fold in R^7, dilated by t, then deforming the resulting compact submanifold of M to the required coassociative 4-fold.

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