The fundamental group of the harmonic archipelago

Abstract

The harmonic archipelago HA is obtained by attaching a large pinched annulus to every pair of consecutive loops of the Hawaiian earring. We clarify the fundamental group pi1(HA) as a quotient of the Hawaiian earring group, provide a precise description of the kernel, show that both pi1(HA) and the kernel are uncountable, and that pi1(HA) has the indiscrete topology.

6 pages

Cited by in corpus (5)

• Topological fundamental groups can distinguish spaces with isomorphic homotopy 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
• A retraction theorem for topological fundamental groups with application to the Hawaiian earring