Current progress on $G_2$--instantons over twisted connected sums
Differential Geometry
2021-04-12 v1
Abstract
We review a method to construct --instantons over compact --manifolds arising as the twisted connected sum of a matching pair of Calabi-Yau -folds with cylindrical end, based on the series of articles [SE15, SEW15, JMPSE17, MNSE17] by the author and others. The construction is based on gluing --instantons obtained from holomorphic bundles over such building blocks, subject to natural compatibility and transversality conditions. Explicit examples are obtained from matching pairs of semi-Fano -folds by an algorithmic procedure based on the Hartshorne-Serre correspondence.
Cite
@article{arxiv.1812.04664,
title = {Current progress on $G_2$--instantons over twisted connected sums},
author = {Henrique N. Sá Earp},
journal= {arXiv preprint arXiv:1812.04664},
year = {2021}
}
Comments
To appear in a forthcoming volume of the Fields Institute Communications, entitled "Lectures and Surveys on G2 manifolds and related topics"