关于在 $$G_2$$ - 轨道上计算平面连接

IF 2.2 1区物理与天体物理 Q1 PHYSICS, MATHEMATICAL

Communications in Mathematical Physics Pub Date : 2024-05-08 DOI:10.1007/s00220-024-05013-7

Langte Ma

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引用次数: 0

摘要

我们研究了无扭$G_2$-orbifolds上（投影）平束上的$G_2$-不定式的模空间。我们证明，在加入小的和一般的整体扰动之后，模空间在不可还原处是紧凑和光滑的。因此，我们定义了在$C^0$-变形下无扭$G_2$-结构不变的$G_2$-卡松不变量。我们计算了乔伊斯构造紧凑 $G_2$-manifolds 时出现的一些轨道折线的这个不变量。

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On Counting Flat Connections Over $$G_2$$ -Orbifolds

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

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来源期刊

Communications in Mathematical Physics 物理-物理：数学物理

CiteScore

4.70

自引率

8.30%

发文量

226

审稿时长

3-6 weeks

期刊介绍： The mission of Communications in Mathematical Physics is to offer a high forum for works which are motivated by the vision and the challenges of modern physics and which at the same time meet the highest mathematical standards.