Work

Recollements of partially wrapped Fukaya categories and surface cuts

Year: 2026

Type: article

Abstract: In this paper we use recollements to investigate partially wrapped Fukaya categories of surfaces with marked points. In particular, we show that cutting surfaces gives rise to recollements of the corresponding partially wrapped Fukaya categories. Our approach is based on a partial cofibrant replacement of a graded quadratic monomial algebra introduced in this paper, and based on the fact that the partially wrapped Fukaya category of a surface with marked points is triangle equivalent to the perfect derived category of a graded gentle algebra with zero differential as shown by Haiden, Katzarkov, and Kontsevich. Using this, we study particular generators of partially wrapped Fukaya categories, namely full exceptional sequences, silting objects, and simple-minded collections. In particular, we fully characterize the existence of full exceptional sequences and we give an example of a partially wrapped Fukaya category which does not admit a silting object, that is the category does not admit a generator whose positive self-extensions vanish.

Source: International Mathematics Research Notices

DOI: 10.1093/imrn/rnag133

Authors: Wen Chang, Haibo Jin, Sibylle Schroll

Institutions: Shaanxi Normal University, East China Normal University, University of Cologne

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Engineering and Physical Sciences Research Council

Award: Graphs in Representation Theory