On Upper Bounds for the Depth of some Classes of Polyhedra

2023/07/29 by Mojtaba Mohareri, Mohareri, Mojtaba, Behrooz Mashayekhy +1
Computer Science · Engineering · Mathematics · #54E30 #55P15 #55P20 #55P55 #55Q20 #Algebraic Topology (math.AT) #Computational Geometry and Mesh Generation #FOS: Mathematics #Mathematics and Applications #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2307.15891

openalex publication_date 2023/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we present upper bounds for the depth of some classes of polyhedra, including: polyhedra with finite fundamental group, polyhedra P with abelian or free π₁(P) and finitely generated H_i(tildeP;ℤ, 2-dimensional polyhedra with abelian or free fundamental group, and 2-dimensional polyhedra with elementary amenable fundamental group G with finite cohomological dimension cd(G). Furthermore, we provide some examples to show that some of these bounds are sharp.

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