Complex G₂-manifolds and Seiberg-Witten Equations

2018/04/26 by Selman Akbulut, Akbulut, Selman, Üstün Yıldırım +1
Mathematics · #53C29 #53C38 #57R57 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1804.09951

openalex publication_date 2018/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce the notion of complex G₂ manifold M_{\mathbb C}, and complexification of a G₂ manifold M⊂ M_{\mathbb C}. As an application we show the following: If (Y,s) is a closed oriented 3-manifold with a Spin^c structure, and (Y,s)⊂ (M, φ) is an imbedding as an associative submanifold of some G₂ manifold (such imbedding always exists), then the isotropic associative deformations of Y in the complexified G₂ manifold M_{\mathbb C} is given by Seiberg-Witten equations.

Citations

• Calibrated associative and Cayley embeddings

Related

• Deformations in G₂ Manifolds
• Calibrated Manifolds and Gauge Theory
• Recent Developments in Seiberg-Witten Theory and Complex Geometry
• Seiberg-Witten-Floer Homology and Gluing Formulae
• Gluing formula for the stable cohomotopy version of Seiberg-Witten invariants along 3-manifolds with b₁ > 0