The cuplength lower bound for Rouquier dimension of wrapped Fukaya categories

Let MM be a smooth manifold, and let Cuplength(M)\operatorname{Cuplength}(M) denote the cuplength of H(M;k)H^*(M;k) for any field kk. Let C(M)\mathcal C(M) denote the wrapped Fukaya category associated to MM. Cuplength conjecture.

Cuplength(M)Rdim(C(M)).\operatorname{Cuplength}(M)\leq \operatorname{Rdim}(\mathcal C(M)).

This conjecture proposes that cuplength gives a lower bound for Rouquier dimension, strengthening the paper's lower bound for generation by the cotangent fiber. The source gives no resolution.

Sources & referencesView supporting material

Primary source

Andrew Hanlon, Jeff Hicks and Oleg Lazarev, “Relating categorical dimensions in topology and symplectic geometry”, arXiv:2308.13677 (2025).

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