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Proceedings of the London Mathematical Society Advance Access originally published online on February 24, 2009
Proceedings of the London Mathematical Society 2009 99(2):297-325; doi:10.1112/plms/pdp004
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© 2009 London Mathematical Society

Hodge theory for G2-manifolds: intermediate Jacobians and Abel–Jacobi maps

Spiro Karigiannis

Department of Pure Mathematics
University of Waterloo
200 University Avenue West
Waterloo
Ontario
Canada
N2L 3G1

Naichung Conan Leung

Institute of Mathematical Sciences and Department of Mathematics
Chinese University of Hong Kong
Shatin
Hong Kong
ncleung@ims.cuhk.edu.hk

Received 19 September 2007. Revision received 11 December 2008.

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-Kähler 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.

2000 Mathematics Subject Classification 53D30 (primary), 53C26, 53C29, 53C38 (secondary).

The research of the second author is partially supported by a research RGC grant from the Hong Kong government.


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