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arXiv:1909.11473 [math.DG]AbstractReferencesReviewsResources

Constructions of compact G2-holonomy manifolds

Alexei Kovalev

Published 2019-09-25Version 1

This is a survey paper. We explain the known constructions for two geometrically different classes of examples of compact Riemannian 7-manifolds with holonomy G2. One method uses resolutions of singularities of appropriately chosen 7-dimensional orbifolds, with the help of asymptotically locally Euclidean spaces. Another method uses the gluing of two asymptotically cylindrical pieces and requires a certain matching condition for their cross-sections `at infinity'.

Comments: To appear in a forthcoming volume of the Fields Institute Communications, entitled "Lectures and Surveys on G2 manifolds and related topics"
Categories: math.DG
Subjects: 53C25, 53C21, 58J60
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