Homotopy groups of symmetric products

Eduardo Blanco-Gómez

Homotopy groups of symmetric products

Algebraic Topology 2023-11-08 v1

Authors: Eduardo Blanco-Gómez

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.

Keywords

homotopy groups symmetric products hausdorff space monomorphism discontinuous homotopy groups topology

Cite

@article{arxiv.2311.04132,
  title  = {Homotopy groups of symmetric products},
  author = {Eduardo Blanco-Gómez},
  journal= {arXiv preprint arXiv:2311.04132},
  year   = {2023}
}

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