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