2017/03/13 by Tolga Etgü, Etgü, Tolga, Yanki Lekili +1 · 2 citations
Mathematics · #FOS: Mathematics #Representation Theory (math.RT) #Symplectic Geometry (math.SG) #math.RT #math.SG
paper · pdf · doi:10.48550/arxiv.1703.04515
29 pages, 10 figures. Clarifications and minor corrections following comments by referees. Notably, the proofs of Theorem 12 and Proposition 14 are made explicit, the connection to deformation quantization is spelled out in Example 6, and Remark 19 about negative plumbings is included
arxiv created 2018/10/12 · arxiv updated 2018/10/15
Given an arbitrary graph Γ and non-negative integers gv for each vertex v of Γ, let XΓ be the Weinstein 4-manifold obtained by plumbing copies of T^*Σv according to this graph, where Σv is a surface of genus gv. We compute the wrapped Fukaya category of XΓ (with bulk parameters) using Legendrian surgery extending our previous work arXiv:1502.07922 where it was assumed that gv=0 for all v and Γ 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 arXiv:math/0404186. Along the way, we find a smaller model for the internal DG-algebra of Ekholm-Ng arXiv:1307.8436 associated to 1-handles in the Legendrian surgery presentation of Weinstein 4-manifolds which might be of independent interest.