Topological fundamental groups can distinguish spaces with isomorphic homotopy groups

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.

5 pages; minor improvements

References in corpus (5)

• The fundamental group of the harmonic archipelago
• The topological Hawaiian earring group does not embed in the inverse limit of free groups
• The Hawaiian earring group is topologically incomplete
• A characterization of spaces with discrete topological fundamental group
• A monomorphism theorem for the inverse limit of nested retracts

Cited by in corpus (6)

• Discreteness and Homogeneity of the Topological Fundamental Group
• The topological Hawaiian earring group does not embed in the inverse limit of free groups
• The Hawaiian earring group is topologically incomplete
• A monomorphism theorem for the inverse limit of nested retracts
• Topological Homotopy Groups
• On fundamental groups with the quotient topology