Comptes Rendus
Article de recherche - Algèbre, Théorie des singularités
Rabinowitz Fukaya categories as cluster categories
[Catégories de Rabinowitz Fukaya en tant que catégories amassées]
Yankı Lekili1 orcid ; Kazushi Ueda2 orcid
1Department of Mathematics, Imperial College London, South Kensington, London, SW7 2AZ, UK
2Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan
Comptes Rendus. Mathématique, Volume 364 (2026), pp. 563-582

We discuss homological mirror symmetry for Rabinowitz Fukaya categories of Milnor fibers of double suspensions of invertible polynomials, and prove it for Brieskorn–Pham polynomials which are not of Calabi–Yau type. This allows a calculation of the Rabinowitz Floer homology of the Milnor fiber as the Hochschild homology of the dg category of equivariant matrix factorizations.

Nous étudions la symétrie miroir homologique pour les catégories de Rabinowitz Fukaya des fibres de Milnor des suspensions doubles de polynômes inversibles, et la prouvons pour les polynômes de Brieskorn–Pham qui ne sont pas de type Calabi–Yau. Cela permet de calculer l’homologie de Rabinowitz Floer de la fibre de Milnor comme l’homologie de Hochschild de la dg-catégorie des factorisations matricielles équivariantes.

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Révisé le :
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DOI : 10.5802/crmath.791
Keywords: Fukaya category, cluster category, homological mirror symmetry, Hochschild cohomology
Mots-clés : Catégorie de Fukaya, catégorie amassée, symétrie miroir homologique, cohomologie de Hochschild

Yankı Lekili  1   ; Kazushi Ueda  2

1 Department of Mathematics, Imperial College London, South Kensington, London, SW7 2AZ, UK
2 Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
Yankı Lekili; Kazushi Ueda. Rabinowitz Fukaya categories as cluster categories. Comptes Rendus. Mathématique, Volume 364 (2026), pp. 563-582. doi: 10.5802/crmath.791
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