{"title":"On Counting Flat Connections Over $$G_2$$ -Orbifolds","authors":"Langte Ma","doi":"10.1007/s00220-024-05013-7","DOIUrl":null,"url":null,"abstract":"<p>We study the moduli space of <span>\\(G_2\\)</span>-instantons on (projectively) flat bundles over torsion-free <span>\\(G_2\\)</span>-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 <span>\\(G_2\\)</span>-Casson invariant that is invariant under <span>\\(C^0\\)</span>-deformation of torsion-free <span>\\(G_2\\)</span>-structures. We compute this invariant for some orbifolds that arise in Joyce’s construction of compact <span>\\(G_2\\)</span>-manifolds.</p>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1007/s00220-024-05013-7","RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
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.
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.