To S. Parsa's theorem on embeddability of joins

2023/02/21 by A. Skopenkov, Skopenkov, A.
Computer Science · Mathematics · #55N91 #57Q35 #Advanced Topology and Set Theory #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Limits and Structures in Graph Theory #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2302.11537

openalex publication_date 2023/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The purpose of this short note is to guide a reader to a reliable reference for the following result of S. Parsa: For any k,l≥2 there exist simplicial complexes K, L of dimensions k,l such that K does not embed into \mathbb R^2k, and L does not embed into \mathbb R^2l, but the join K*L embeds into \mathbb R^2(k+l+1).

Related

• On embeddability of joins and their `factors'
• Instability of the Smith Index Under Joins and Applications to Embeddability
• Embeddability of joinpowers, and minimal rank of partial matrices
• Joins for (Augmented) Simplicial Sets
• Fungible obstructions to embedding 2-complexes