2016/01/31 by Lizhen Qin, Botong Wang
Mathematics · #Betti number #Diffeomorphism #Fundamental group #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy #Homotopy and Cohomology in Algebraic Topology #Homotopy group #Space (punctuation) #Symplectic geometry #Topology (electrical circuits) #math.AG #math.CV #math.SG #msc:32J27 #msc:53D05 #n-connected
paper · pdf · doi:10.2140/gt.2018.22.2115
published as Geom. Topol. 22 (2018) 2115-2144 · Final version. To appear in Geometry and Topology
openalex created_date 2016/06/24 · arxiv created 2017/12/05 · openalex publication_date 2018/04/05 · arxiv updated 2018/04/18 · openalex updated_date 2026/08/05
We construct a family of [math] –dimensional compact manifolds [math] which are simultaneously diffeomorphic to complex Calabi–Yau manifolds and symplectic Calabi–Yau manifolds. They have fundamental groups [math] , their odd-degree Betti numbers are even, they satisfy the hard Lefschetz property, and their real homotopy types are formal. However, [math] is never homotopy equivalent to a compact Kähler manifold for any topological space [math] . The main ingredient to show the non-Kählerness is a structure theorem of cohomology jump loci due to the second author.