Thin instantons in G_2-manifolds and Seiberg-Witten invariants

TL;DR

This paper constructs thin instantons in G_2-manifolds with boundaries on coassociative submanifolds, linking their properties to Seiberg-Witten invariants via J-holomorphic curves.

Contribution

It introduces a novel method to construct thin instantons from J-holomorphic curves and relates them to Seiberg-Witten invariants in G_2-geometry.

Findings

Construction of thin instantons from J-holomorphic curves

Relationship established between instantons and Seiberg-Witten invariants

Provides new insights into G_2-manifold topology

Abstract

For two nearby disjoint coassociative submanifolds C and C' in a G_2-manifold, we construct thin instantons with boundaries lying on C and C' from regular J-holomorphic curves in C. We explain their relationship with the Seiberg-Witten invariants for C.