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Fukaya categories of plumbings and multiplicative preprojective algebras

Research output: Contribution to journalArticle

Tolga Etgu, Yanki Lekili

Original languageEnglish
Pages (from-to)777-813
Number of pages37
JournalQuantum Topology
Issue number4
Early online date2 Feb 2019
Accepted/In press2 Feb 2019
E-pub ahead of print2 Feb 2019


King's Authors


Given an arbitrary graph г and non-negative integers g v for each vertex v of г, let X г be the Weinstein 4-manifold obtained by plumbing copies of T *Σ v according to this graph, where Σ v is a surface of genus g v. We compute the wrapped Fukaya category of X г (with bulk parameters) using Legendrian surgery extending our previous work [14] where it was assumed that g v = 0 for all v and г was a tree. The resulting algebra is recognized as the (derived) multiplicative preprojective algebra (and its higher genus version) defined by Crawley-Boevey and Shaw [8]. Along the way, we find a smaller model for the internal DG-algebra of Ekholm and Ng [12] associated to 1-handles in the Legendrian surgery presentation of Weinstein 4-manifolds which might be of independent interest.

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