Asymptotically Conical Associative 3-folds

Abstract

Given an associative 3-fold in R^7 which is asymptotically conical with generic rate less than 1, we show that its moduli space of deformations is locally homeomorphic to the kernel of a smooth map between smooth manifolds. Moreover, the virtual dimension of the moduli space is computed and shown to be non-negative for rates greater than -1, whereas the associative 3-fold is expected to be isolated for rates less than or equal to -1.

33 pages, v2: major changes for published version, mainly regarding the twisted Dirac and d-bar operators

References in corpus (5)

• The geometric complexity of special Lagrangian $T^2$-cones
• Deformations of associative submanifolds with boundary
• Deformation Theory of Asymptotically Conical Coassociative 4-folds
• Calibrated Submanifolds of R^7 and R^8 with Symmetries
• Deformations of Asymptotically Cylindrical Coassociative Submanifolds with Moving Boundary

Cited by in corpus (4)

• Deformation theory of G_2 conifolds
• Deformations of calibrated subbundles of Euclidean spaces via twisting by special sections
• Conjectures on counting associative 3-folds in $G_2$-manifolds
• Deformations of Asymptotically Conical $G_2$-Instantons