2024/06/20 by Biplab Basak, Raju Kumar Gupta, Basak, Biplab +1
Computer Science · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Markov Chains and Monte Carlo Methods #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2406.14010
openalex publication_date 2024/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In their work [10], Feng Luo and Richard Stong introduced the concept of the average edge order, denoted as μ0(K). They demonstrated that if μ0(K)≤ (9)/(2) for a closed 3-manifold K, then K must be a sphere. Building upon this foundation, Makoto Tamura extended similar results to 3-manifolds with non-empty boundaries in [12,13]. In our present study, we extend these findings to normal 3-pseudomanifolds. Specifically, we establish that for a normal 3-pseudomanifold K with singularities, μ0(K)≥(30)/(7). Moreover, equality holds if and only if K is a one-vertex suspension of a triangulation of \mathbbRP2 with seven vertices. Furthermore, we establish that when (30)/(7)≤μ0(K)≤(9)/(2), the 3-pseudomanifold K can be derived from some boundary complexes of 4-simplices by a sequence of possible operations, including connected sums, bistellar 1-moves, edge contractions, edge expansions, vertex folding, and edge folding.