On Counting Flat Connections over G₂-Orbifolds

2023/04/02 by Ma, Langte
#Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2304.00606

Abstract

We study the moduli space of G₂-instantons on (projectively) flat bundles over torsion-free G₂-orbifolds. We prove that the moduli space is compact and smooth at the irreducible locus after adding small and generic holonomy perturbations. Consequently, we define an integer-valued invariant that is invariant under C⁰-deformation of torsion-free G₂-structures. We compute this invariant for some orbifolds that arise in Joyce's construction of compact G₂-manifolds

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