Constructions of compact G2-holonomy manifolds
Differential Geometry
2019-09-26 v1
Abstract
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'.
Cite
@article{arxiv.1909.11473,
title = {Constructions of compact G2-holonomy manifolds},
author = {Alexei Kovalev},
journal= {arXiv preprint arXiv:1909.11473},
year = {2019}
}
Comments
To appear in a forthcoming volume of the Fields Institute Communications, entitled "Lectures and Surveys on G2 manifolds and related topics"