Hodge Theory for G2-manifolds: Intermediate Jacobians and Abel-Jacobi maps

Abstract

We study the moduli space of torsion-free G2-structures on a fixed compact manifold, and define its associated universal intermediate Jacobian J. We define the Yukawa coupling and relate it to a natural pseudo-Kahler structure on J. We consider natural Chern-Simons type functionals, whose critical points give associative and coassociative cycles (calibrated submanifolds coupled with Yang-Mills connections), and also deformed Donaldson-Thomas connections. We show that the moduli spaces of these structures can be isotropically immersed in J by means of G2-analogues of Abel-Jacobi maps.

arXiv comment31 pages. Version 2: added a reference and some remarks. Version 3: Incorporated the referee's suggestions. Final version to appear in Proceedings of the London Mathematical Society

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• Deformations of glued G_2-manifolds
• On the incompleteness of $G_2$-moduli spaces along degenerating families of $G_2$-manifolds
• Deformed $G_2$-instantons on ${\mathbb{R}}^4\times S^3$
• Examples of deformed Spin(7)-instantons/Donaldson-Thomas connections
• $L^2$ harmonic forms on complete special holonomy manifolds
• Geometry and periods of $G_2$-moduli spaces
• The Space of Closed $G_2$-Structures. I. Connections
• Conformal transformations of the pseudo-Riemannian metric of a homogeneous pair