Fukaya categories of plumbings and multiplicative preprojective algebras

  • Tolga Etgü

    Koç University, Istanbul, Turkey
  • Yankı Lekili

    King's College London, UK
Fukaya categories of plumbings and multiplicative preprojective algebras cover
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Abstract

Given an arbitrary graph and non-negative integers for each vertex of , let be the Weinstein 4-manifold obtained by plumbing copies of according to this graph, where is a surface of genus . We compute the wrapped Fukaya category of (with bulk parameters) using Legendrian surgery extending our previous work [14] where it was assumed that for all and 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.

Cite this article

Tolga Etgü, Yankı Lekili, Fukaya categories of plumbings and multiplicative preprojective algebras. Quantum Topol. 10 (2019), no. 4, pp. 777–813

DOI 10.4171/QT/131