Computing ν-invariants of Joyce's compact G₂-manifolds

2020/08/17 by Christopher Scaduto, Scaduto, Christopher
Computer Science · Mathematics · #58J28 #Advanced Operator Algebra Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2008.07239

openalex publication_date 2020/08/17 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28

Abstract

Crowley and Nordström introduced an invariant of G₂-structures on the tangent bundle of a closed 7-manifold, taking values in the integers modulo 48. Using the spectral description of this invariant due to Crowley, Goette and Nordström, we compute it for many of the closed torsion-free G₂-manifolds defined by Joyce's generalized Kummer construction.

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• Distinguishing G₂-manifolds
• Recent results on closed G₂-structures
• Improved Estimates for G₂-structures on the Generalised Kummer Construction
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