Topological fundamental groups can distinguish spaces with isomorphic homotopy groups
Algebraic Topology
2007-05-23 v2 General Topology
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.
Cite
@article{arxiv.math/0502402,
title = {Topological fundamental groups can distinguish spaces with isomorphic homotopy groups},
author = {Paul Fabel},
journal= {arXiv preprint arXiv:math/0502402},
year = {2007}
}
Comments
5 pages; minor improvements