2019/03/11 by A. Bahri, Bahri, A., M. Bendersky +3 · 2 citations
Computer Science · Mathematics · #13F55 #35S22 #52B11 #52C35 #55P42 #55Q15 #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #History and Overview (math.HO) #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1903.04114
openalex publication_date 2019/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A polyhedral product is a natural subspace of a Cartesian product that is specified by a simplicial complex. The modern formalism arose as a generalization of the spaces known as moment-angle complexes which were developed within the nascent subject of toric topology. This field, which began as a topological approach to toric geometry and aspects of symplectic geometry, has expanded rapidly in recent years. The investigation of polyhedral products and their homotopy theoretic properties has developed to the point where they are studied in various fields of mathematics far removed from their origin. In this survey, we provide a brief historical overview of the development of this subject, summarize many of the main results and describe applications.