SKEW-GROUP A ∞ -CATEGORIES AS FUKAYA CATEGORIES OF ORBIFOLDS - CNRS - Centre national de la recherche scientifique
Pré-Publication, Document De Travail Année : 2024

SKEW-GROUP A ∞ -CATEGORIES AS FUKAYA CATEGORIES OF ORBIFOLDS

Pierre Guy Plamondon
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Résumé

We study the partially wrapped Fukaya category of a surface with boundary with an action of a group of order two. Inspired by skew-group algebras and categories, we define the notion of a skew-group A∞-category and let it play the role of the partially wrapped Fukaya category of an orbifold surface. We classify indecomposable objects in terms of graded curves with signs, or taggings, at orbifold points. We compute morphisms between a class of objects, and we use this to describe tilting objects and find algebras derivedequivalent to skew-gentle algebras.

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Dates et versions

hal-04708076 , version 1 (24-09-2024)

Identifiants

  • HAL Id : hal-04708076 , version 1

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Claire Amiot, Pierre Guy Plamondon. SKEW-GROUP A ∞ -CATEGORIES AS FUKAYA CATEGORIES OF ORBIFOLDS. 2024. ⟨hal-04708076⟩
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