TY - JOUR
T1 - Higher dimensional knot spaces for manifolds with vector cross products
AU - Lee, Jae Hyouk
AU - Leung, Naichung Conan
N1 - Funding Information:
The research of the first author is partially supported by NSF/DMS-0103355, Direct Grant from CUHK and RGC Earmarked Grants of Hong Kong. Authors express their gratitude to the referee for useful comments to improve the presentation of this article.
PY - 2007/8/1
Y1 - 2007/8/1
N2 - 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.
AB - 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.
KW - Branes
KW - Holomorphic symplectic spaces on isotropic knot spaces
KW - Instantons
KW - Symplectic structures on knot spaces
KW - Vector cross product
UR - http://www.scopus.com/inward/record.url?scp=34247198269&partnerID=8YFLogxK
U2 - 10.1016/j.aim.2006.12.003
DO - 10.1016/j.aim.2006.12.003
M3 - Article
AN - SCOPUS:34247198269
VL - 213
SP - 140
EP - 164
JO - Advances in Mathematics
JF - Advances in Mathematics
SN - 0001-8708
IS - 1
ER -