2020/02/21 by Frank Reidegeld, Reidegeld, Frank
Mathematics · #14J28 #53C29 #Abelian group #Action (physics) #Betti number #Combinatorics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry #Geometry and complex manifolds #Gravitational singularity #Group (periodic table) #Holonomy #Manifold (fluid mechanics) #Mathematical analysis #Mathematics #Physics #Product (mathematics) #Pure mathematics #Quotient #Torsion (gastropod) #Torus #math.DG #msc:14J28 #msc:53C29
paper · pdf · doi:10.48550/arxiv.2002.09231
published in arXiv (Cornell University) (Cornell University) · 37 pages
arxiv created 2020/02/21 · openalex publication_date 2020/02/21 · arxiv updated 2020/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A product of a K3 surface S and a flat 3-dimensional torus T3 is a manifold with holonomy SU(2). Since SU(2) is a subgroup of G2, S× T3 carries a torsion-free G2-structure. We assume that S admits an action of ℤ22 with certain properties. There are several possibilities to extend this action to S× T3. A recent result of Joyce and Karigiannis allows us to resolve the singularities of (S× T3)/ℤ22 such that we obtain smooth G2-manifolds. We classify the quotients (S× T3)/ℤ22 under certain restrictions and compute the Betti numbers of the corresponding G2-manifolds. Moreover, we study a class of quotients by a non-abelian group. Several of our examples have new values of (b2,b3).