G2-manifolds的Hodge理论：中间Jacobian和Abel-Jacobi映射
Hodge Theory for G2-manifolds: Intermediate Jacobians and Abel-Jacobi maps
摘要：
研究了固定紧致流形上无挠G2-结构的模空间，定义了它的泛中间Jacobian J，定义了Yukawa耦合，并将它与J上的自然伪Kahler结构联系起来，考虑了自然Chern-Simons型泛函，其临界点给出了结合圈和余结合圈（校准子流形与杨-米尔斯连接耦合），以及变形唐纳森-托马斯连接。我们证明了这些结构的模空间可以通过Abel-Jacobi映射的G2-类似物各向同性地浸入J中。
英文摘要：
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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