Abstract.
Suppose that N is a compact coassociative 4-fold with a conical singularity in a 7-manifold M, with a G2 structure given by a closed 3-form. We construct a smooth family, {N′(t) : t ∈ (0,τ)} for some τ > 0, of compact, nonsingular, coassociative 4-folds in M which converge to N in the sense of currents, in geometric measure theory, as t → 0. This realisation of desingularizations of N is achieved by gluing in an asymptotically conical coassociative 4-fold in \({\mathbb{R}}^7\), dilated by t, then deforming the resulting compact 4-dimensional submanifold of M to the required coassociative 4-fold.
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Received: March 2007 Revision: June 2007 Accepted: June 2007
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Lotay, J.D. Desingularization of Coassociative 4-Folds with Conical Singularities. GAFA Geom. funct. anal. 18, 2055–2100 (2009). https://doi.org/10.1007/s00039-009-0711-1
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DOI: https://doi.org/10.1007/s00039-009-0711-1