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Hodge theory for G2 manifolds: Intermediate Jacobians and Abel-Jacabi maps

Conan Leung Chinese Univ of HK Spiro Karigiannis Univ of Waterloo

Differential Geometry mathscidoc:1608.10087

Proc. LMS, 99, 297-325, 2009
We study the moduli space M of torsion-free G2-structures on a fixed compact manifold M7, and define its associated universal intermediate Jacobian J . We define the Yukawa coupling and relate it to a natural pseudo-K¨ahler 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.
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@inproceedings{conan2009hodge,
  title={Hodge theory for G2 manifolds: Intermediate Jacobians and Abel-Jacabi maps},
  author={Conan Leung, and Spiro Karigiannis},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160830144713172207563},
  booktitle={Proc. LMS},
  volume={99},
  pages={297-325},
  year={2009},
}
Conan Leung, and Spiro Karigiannis. Hodge theory for G2 manifolds: Intermediate Jacobians and Abel-Jacabi maps. 2009. Vol. 99. In Proc. LMS. pp.297-325. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160830144713172207563.
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