2007/09/30 by Spiro Karigiannis, Naichung Conan Leung · 1 citation
Mathematics · #Advanced Algebra and Geometry #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #math.DG #math.SG #msc:53C26 #msc:53C29 #msc:53C38 #msc:53D30
paper · pdf · doi:10.1112/plms/pdp004
published as Proceedings of the London Mathematical Society (3) 99, 297-325 (2009) · 31 pages. Version 2: added a reference and some remarks. Version 3: Incorporated the referee's suggestions. Final version to appear in Proceedings of the London Mathematical Society
arxiv created 2009/01/27 · openalex publication_date 2009/02/24 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29
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.