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arXiv · 0709.2987

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

Spiro Karigiannis·Naichung Conan Leung
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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.

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Spiro Karigiannis, Naichung Conan Leung. 2009-01-27. Hodge Theory for G2-manifolds: Intermediate Jacobians and Abel-Jacobi maps. https://doi.org/10.1112/plms%2Fpdp004

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