Homotopy groups of symmetric products

2023/11/07 by Eduardo Blanco-Gómez, Blanco-Gómez, Eduardo
Decision Sciences · Mathematics · #Advanced Topology and Set Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Fuzzy and Soft Set Theory #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2311.04132

openalex publication_date 2023/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we prove that, taking X a Hausdorff topological space, the homotopy groups of the spaces SP_m(X) and F_m(X), both called symmetric products, are monomorphic. We also introduce a new algebraic tool in topology: the discontinuous homotopy groups.

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