On Counting Flat Connections Over $G_2$-Orbifolds

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发表日期：

2024年5月8日

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Langte Ma

摘要

We study the moduli space of $G_2$ $G_{2}$ -instantons on (projectively) flat bundles over torsion-free $G_2$ $G_{2}$ -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 the $G_2$ $G_{2}$ -Casson invariant that is invariant under $C^0$ $C^{0}$ -deformation of torsion-free $G_2$ $G_{2}$ -structures. We compute this invariant for some orbifolds that arise in Joyce’s construction of compact $G_2$ $G_{2}$ -manifolds.

On Counting Flat Connections Over \(G_2\)-Orbifolds

摘要