Topological fundamental groups can distinguish spaces with isomorphic homotopy groups

Paul Fabel

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Topological fundamental groups can distinguish spaces with isomorphic homotopy groups

Paul Fabel

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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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BibTeX RIS

Paul Fabel. 2005-04-19. Topological fundamental groups can distinguish spaces with isomorphic homotopy groups. https://arxiv.org/abs/math/0502402

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