Compactification and uniform orientability conjecture for open-curve moduli spaces
Compactification and uniform orientability conjecture for open-curve moduli spaces
Let be a manifold with symplectic form and compatible almost complex structure , let be transversely meeting Lagrangian submanifolds, and let be a holomorphic curve with boundary components and marked boundary points mapping to Lagrangian intersection points. For a fixed homotopy class , denote by the moduli space of holomorphic maps in that class. Compactification and uniform orientability conjecture. The moduli space admits a compactification to an orientable manifold with corners, and an orientation can be chosen uniformly for all . Such compactified and coherently oriented moduli spaces are intended to provide the geometric foundation for the stringy-category equations. The supplied text gives no resolution.
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Primary source
M. V. Movshev, “Fukaya category with curves of higher genus”, arXiv:math/9911123 (1999).
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