2017/10/31 by Yin Li · 1 citation
Mathematics · #math.SG #math.AT #math.RT
paper · pdf · doi:10.1112/topo.12113
68 pages, 23 figures; v6: final version, accepted by Journal of Topology
arxiv created 2019/05/30 · arxiv updated 2019/07/03
Let M be a Liouville 6-manifold which is the smooth fiber of a Lefschetz fibration on ℂ4 constructed by suspending a Lefschetz fibration on ℂ3. We prove that for many examples including stabilizations of Milnor fibers of hypersurface cusp singularities, the compact Fukaya category F(M) and the wrapped Fukaya category W(M) are related through A_∞-Koszul duality, by identifying them with cyclic and Calabi-Yau completions of the same quiver algebra. This implies the split-generation of the compact Fukaya category F(M) by vanishing cycles. Moreover, new examples of Liouville manifolds which admit quasi-dilations in the sense of Seidel-Solomon are obtained.