Restriction functor conjecture for Liouville subdomains

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Let Min⊂MM^{in} \subset M be an inclusion of Liouville subdomains, and let \EuScriptW(M)\EuScript{W}(M) denote the wrapped Fukaya category of MM, with Tw⁡(\EuScriptW(Min))\operatorname{Tw}(\EuScript{W}(M^{in})) its category of twisted complexes. Restriction functor conjecture. Any inclusion of a Liouville subdomain Min⊂MM^{in} \subset M induces an A∞A_{\infty} restriction functor

\EuScriptW(M)→Tw⁡(\EuScriptW(Min)).\EuScript{W}(M) \to \operatorname{Tw}(\EuScript{W}(M^{in})).

The conjecture extends the restriction construction for Liouville subdomains to arbitrary inclusions, with the image generally landing in twisted complexes rather than the wrapped Fukaya category itself. The source does not provide evidence resolving the conjecture.

References

Primary source

Mohammed Abouzaid, “On the wrapped Fukaya category and based loops”, arXiv:0907.5606 (2010).

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