Topological fundamental groups can distinguish spaces with isomorphic homotopy groups

Details Topological fundamental groups can distinguish spaces with isomorphic homotopy groups Topological fundamental groups can distinguish spaces with isomorphic homotopy groups

2005-02-18

arxiv.org/abs/math/0502402v2

Mathematics

Algebraic Topology

5 pages; minor improvements

Scientific paper

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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