2022/02/14 by Biplab Basak, Raju Kumar Gupta, Basak, Biplab +3 · 1 citation
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2202.06582
Let Δ be a g2-minimal normal 3-pseudomanifold. A vertex in Δ whose link is not a sphere is called a singular vertex. When Δ contains at most two singular vertices, its combinatorial characterization is known [9]. In this article, we present a combinatorial characterization of such a Δ when it has three singular vertices, including one \mathbbRP2-singularity, or four singular vertices, including two \mathbbRP2-singularities. In both cases, we prove that Δ is obtained from a one-vertex suspension of a surface, and some boundary complexes of 4-simplices by applying the combinatorial operations of types connected sums, vertex foldings, and edge foldings.