Generation of the wrapped Fukaya category of the pair of pants

Let Πn(C)n+1\Pi_n\subset(\mathbb{C}^*)^{n+1} be the nn-dimensional pair of pants, and let L{i}L_{\{i\}}, for i=0,1,,n+1i=0,1,\dots,n+1, be the specified objects of its wrapped Fukaya category. Pair-of-pants generation conjecture. The category W(Πn)\mathcal{W}(\Pi_n) should be split-generated by the objects L{i}L_{\{i\}}, i=0,1,,n+1i=0,1,\dots,n+1. This generation statement is attributed to work in progress of Zack Sylvan and is used in the paper's proposed inductive proof of homological mirror symmetry for pairs of pants; it is not presented as fully established in the source.

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Primary source

Denis Auroux, “Speculations on homological mirror symmetry for hypersurfaces in (C^*)^n”, arXiv:1705.06667 (2017).

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