Compactification and uniform orientability conjecture for open-curve moduli spaces

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Let MM be a manifold with symplectic form ω\omega and compatible almost complex structure JJ, let L1(j),,Lpj(j)L_1(j),\dots,L_{p_j}(j) be transversely meeting Lagrangian submanifolds, and let XX be a holomorphic curve with boundary components and marked boundary points mapping to Lagrangian intersection points. For a fixed homotopy class [f][f], denote by M(f)M(f) the moduli space of holomorphic maps in that class. Compactification and uniform orientability conjecture. The moduli space M(f)M(f) admits a compactification to an orientable manifold M~(f)\tilde M(f) with corners, and an orientation can be chosen uniformly for all M~(f)\tilde M(f). 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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Sources & referencesView supporting material

Primary source

M. V. Movshev, “Fukaya category with curves of higher genus”, arXiv:math/9911123 (1999).

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