Desingularization of coassociative 4-folds with conical singularities: Obstructions and applications

Lotay, Jason

doi:10.1090/S0002-9947-2014-06193-X

Desingularization of coassociative 4-folds with conical singularities: Obstructions and applications
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Trans. Amer. Math. Soc. 366 (2014), 6051-6092 Request permission

Abstract:

We study the problem of desingularizing coassociative conical singularities via gluing, allowing for topological and analytic obstructions, and discuss applications. This extends previous work of the author on the unobstructed case. We interpret the analytic obstructions geometrically via the obstruction theory for deformations of conically singular coassociative 4-folds, and thus relate them to the stability of the singularities. We use our results to describe the relationship between moduli spaces of coassociative 4-folds with conical singularities and those of their desingularizations. We also apply our theory in examples, including the known conically singular coassociative 4-folds in compact holonomy $\mathrm {G}_2$ manifolds.

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