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

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

2007-09-19

arxiv.org/abs/0709.2987v3

Proceedings of the London Mathematical Society (3) 99, 297-325 (2009)

Mathematics

Differential Geometry

31 pages. Version 2: added a reference and some remarks. Version 3: Incorporated the referee's suggestions. Final version to a

Scientific paper

10.1112/plms/pdp004

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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