Relation between finite topological spaces and finitely presentable groups

2020/12/31 by Roldán, Samuel, Mora, Jose Luis, Becerra, Edward
#Algebraic Topology (math.AT) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2012.15395

Abstract

In this paper it is shown how to construct a finite topological space X for a given finitely presentable group G such that π₁(X)≅ 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.

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