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


Author: Jason D. Lotay
Journal: Trans. Amer. Math. Soc. 366 (2014), 6051-6092
MSC (2010): Primary 53C38
DOI: https://doi.org/10.1090/S0002-9947-2014-06193-X
Published electronically: May 23, 2014
MathSciNet review: 3256193
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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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Additional Information

Jason D. Lotay
Affiliation: Department of Mathematics, University College London, London, England

DOI: https://doi.org/10.1090/S0002-9947-2014-06193-X
Received by editor(s): September 25, 2012
Received by editor(s) in revised form: March 26, 2013
Published electronically: May 23, 2014
Additional Notes: The author was supported by an EPSRC Career Acceleration Fellowship
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.