$G_2$-instantons on noncompact $G_2$-manifolds: results and open problems
Abstract
We survey the known existence and non-existence results for $G_2$-instantons on non-compact cohomogeneity-1 $G_2$-manifolds and their consequences, including an explicit example of a family of $G_2$-instantons where bubbling, removable singularities and conservation of energy phenomena occur. We also describe several open problems for future research.
- Publication:
-
arXiv e-prints
- Pub Date:
- December 2018
- DOI:
- arXiv:
- arXiv:1812.11867
- Bibcode:
- 2018arXiv181211867L
- Keywords:
-
- Mathematics - Differential Geometry;
- Mathematical Physics;
- 53C07;
- 53C25
- E-Print:
- To appear in a forthcoming volume of the Fields Institute Communications, entitled "Lectures and Surveys on G2 manifolds and related topics"