Topological fundamental groups can distinguish spaces with isomorphic homotopy groups

2005/02/18 by Paul Fabel, Fabel, Paul
Mathematics · #55P15 #Algebraic Topology (math.AT) #FOS: Mathematics #General Topology (math.GN) #math.AT #math.GN #msc:55P15

paper · pdf · doi:10.48550/arxiv.math/0502402

5 pages; minor improvements

arxiv created 2005/04/19 · arxiv updated 2009/12/01

Abstract

We exhibit a map f between aspherical spaces X and Y such that f induces an isomorphism on homotopy groups but, with natural topologies, X and Y fail to have homeomorphic fundamental groups. Thus the topological fundamental group has the capacity to distinguish homotopy type when the Whitehead theorem fails.

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