Associative submanifolds in twisted connected sum G₂-manifolds

2022/08/31 by Bera, Gorapada
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2209.00156

Abstract

We introduce a method to construct closed rigid associative submanifolds in twisted connected sum G₂-manifolds. More precisely, we prove a gluing theorem of asymptotically cylindrical (ACyl) associative submanifolds in ACyl G₂-manifolds under a hypothesis. This is analogous to the gluing theorem for G₂-instantons introduced in [SW15]. We rephrase the hypothesis in the special cases where the ACyl associative submanifolds are obtained from holomorphic curves or special Lagrangians in ACyl Calabi-Yau 3-folds. In this way we find many new associative submanifolds which are diffeomorphic to S³, \mathbf R\mathbf P³ or \mathbf R\mathbf P³#\mathbf R\mathbf P³.

Related

• Deformations of asymptotically cylindrical associative submanifolds
• Associative submanifolds of a G2 manifold
• Counting Associatives in Compact G₂ Orbifolds
• Instantons in G2 manifolds from J-holomorphic curves in coassociative submanifolds
• Deformations in G₂ Manifolds