Refined symplectic-cohomology formula for small Q-factorializations

Let YXY \to X be a small \bQ\bQ-factorialization of a compound Du Val singularity PXP \in X. Let \ell be the number of irreducible components of the exceptional locus, let \Uv\Uv be the Milnor fiber of PXP \in X, and let \Uv1,,\Uvr\Uv_1,\ldots,\Uv_r be the Milnor fibers of the resulting \bQ\bQ-factorial singularities Q1,,QrYQ_1,\ldots,Q_r \in Y. Refined Evans–Lekili conjecture. For every i<0i<0,

dim\SHi(\Uv)=j=1rdim\SHi(\Uvj)+.\dim \SH^i(\Uv)=\sum_{j=1}^r\dim \SH^i(\Uv_j)+\ell.

This refinement is based on unpublished calculations and is proposed as a strengthening of the preceding conjecture; its resolution status is not given.

Sources & referencesView supporting material

Primary source

Yanki Lekili and Kazushi Ueda, “Rabinowitz Fukaya categories as cluster categories”, arXiv:2406.15915 (2026).

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