%0 Journal Article
%T Topological fundamental groups can distinguish spaces with isomorphic homotopy groups
%A Paul Fabel
%J Mathematics
%D 2005
%I arXiv
%X 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.
%U http://arxiv.org/abs/math/0502402v2