Examples of Coassociative 4-folds with Conical Singularities

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

2009-10-27

arxiv.org/abs/0910.5092v1

Mathematics

Differential Geometry

32 pages

Scientific paper

In this article we construct examples of coassociative 4-folds with conical singularities in compact manifolds with G_2 holonomy. We apply a method for constructing compact holonomy G_2 manifolds given in arXiv:math/0012189 and deformation theory results from the author's paper arXiv:math/0601762 to achieve our goal. The essential new ingredient is an understanding of the stability of some coassociative conical singularities which arise from complex surface geometry. The work in this article provides a natural first step in trying to construct calibrated fibrations of compact manifolds with G_2 holonomy.

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