Relation between finite topological spaces and finitely presentable groups

Samuel Roldán; Jose Luis Mora; Edward Becerra

Relation between finite topological spaces and finitely presentable groups

Algebraic Topology 2021-01-01 v1 Group Theory

Authors: Samuel Roldán , Jose Luis Mora , Edward Becerra

Abstract

In this paper it is shown how to construct a finite topological space $X$ for a given finitely presentable group $G$ such that $\pi_1(X)\cong G$ . Our construction is not optimal in the sense that the cardinality of the space $X$ might not be the smallest possible. Our main result applies to a large class of interesting groups, including all finite groups.

Keywords

general topology topological groups finite group theory

Cite

@article{arxiv.2012.15395,
  title  = {Relation between finite topological spaces and finitely presentable groups},
  author = {Samuel Roldán and Jose Luis Mora and Edward Becerra},
  journal= {arXiv preprint arXiv:2012.15395},
  year   = {2021}
}

Comments

12 pages, 3 figures

Relation between finite topological spaces and finitely presentable groups

Abstract

Keywords

Cite

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