Gauge Theory in higher dimensions, II

2009/02/18 by Simon Donaldson, Donaldson, Simon, Ed Segal +1 · 3 citations
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.DG

paper · pdf · doi:10.48550/arxiv.0902.3239

arxiv created 2009/02/18 · openalex publication_date 2009/02/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The main aim of the paper is to develop the "Floer theory" associated to Calabi-Yau 3-folds, exending the analogy of Thomas' "holomorphic Casson invariant". The treatment in the body of the paper is largely formal, assuming appropriate compactness properties of moduli spaces of G₂-instantons, but in the last section we make some remarks about these compactness isssues. Section 3 of the paper contains a general dscussion of deformations of the equations, for gauge field and submanifolds, associated to manifolds with exceptional holonomy.

Cited by

• Deformations of asymptotically cylindrical associative submanifolds
• The large mass limit of monopoles: abelian limits and Dirac singularities
• L² harmonic forms on complete special holonomy manifolds

Related

• Categorification of invariants in gauge theory and sypmplectic geometry
• Floer homologies for Lagrangian intersections and instantons
• Stable Yang-Mills connections on Special Holonomy Manifolds
• Holomorphic Floer theory and Donaldson-Thomas invariants
• Yang-Mills connections on G₂-manifolds and Calabi-Yau 3-folds