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.
Keywords
Cite
@article{arxiv.0709.2987,
title = {Hodge Theory for G2-manifolds: Intermediate Jacobians and Abel-Jacobi maps},
author = {Spiro Karigiannis and Naichung Conan Leung},
journal= {arXiv preprint arXiv:0709.2987},
year = {2009}
}
Comments
31 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