JournalsqtVol. 10 , No. 4pp. 777–813

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 Γ\Gamma and non-negative integers gvg_v for each vertex vv of Γ\Gamma, let XΓX_\Gamma be the Weinstein 4-manifold obtained by plumbing copies of TΣvT^*\Sigma_v according to this graph, where Σv\Sigma_v is a surface of genus gvg_v. We compute the wrapped Fukaya category of XΓX_\Gamma (with bulk parameters) using Legendrian surgery extending our previous work [14] where it was assumed that gv=0g_v=0 for all vv and Γ\Gamma 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