Current progress on $G_2$--instantons over twisted connected sums

Henrique N. Sá Earp

doi:10.1007/978-1-0716-0577-6_14

paper

Current progress on $G_{2}$ --instantons over twisted connected sums

arXiv:1812.04664 · doi:10.1007/978-1-0716-0577-6_14

Abstract

We review a method to construct $G_{2}$ --instantons over compact $G_{2}$ --manifolds arising as the twisted connected sum of a matching pair of Calabi-Yau $3$ -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 $G_{2}$ --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 $3$ -folds by an algorithmic procedure based on the Hartshorne-Serre correspondence.

To appear in a forthcoming volume of the Fields Institute Communications, entitled "Lectures and Surveys on G2 manifolds and related topics"

References in corpus (1)

$G_{2}$ -instantons over twisted connected sums: an example

Cited by in corpus (1)

Isolated singularities in $G_{2}$ -structures with torsion

Current progress on G2​--instantons over twisted connected sums

Abstract

References in corpus (1)

Cited by in corpus (1)

Current progress on $G_{2}$ --instantons over twisted connected sums