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Higher dimensional knot spaces for manifolds with vector cross products

Conan Leung Chinese Univ of HK Jae-Hyouk Lee Washington University

Differential Geometry mathscidoc:1608.10091

Advances in Math, 213, 140-164, 2007
Vector cross product structures on manifolds include symplectic, volume, G2- and Spin(7)-structures. We show that the knot spaces of such manifolds have natural symplectic structures, and relate instantons and branes in these manifolds to holomorphic disks and Lagrangian submanifolds in their knot spaces. For the complex case, the holomorphic volume form on a Calabi–Yau manifold defines a complex vector cross product structure. We show that its isotropic knot space admits a natural holomorphic symplectic structure.We also relate the Calabi–Yau geometry of the manifold to the holomorphic symplectic geometry of its isotropic knot space.
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@inproceedings{conan2007higher,
  title={Higher dimensional knot spaces for manifolds with vector cross products},
  author={Conan Leung, and Jae-Hyouk Lee},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160831103844942167567},
  booktitle={Advances in Math},
  volume={213},
  pages={140-164},
  year={2007},
}
Conan Leung, and Jae-Hyouk Lee. Higher dimensional knot spaces for manifolds with vector cross products. 2007. Vol. 213. In Advances in Math. pp.140-164. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160831103844942167567.
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