The fundamental group of the harmonic archipelago
Algebraic Topology
2007-05-23 v1 General Topology
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.
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Cite
@article{arxiv.math/0501426,
title = {The fundamental group of the harmonic archipelago},
author = {Paul Fabel},
journal= {arXiv preprint arXiv:math/0501426},
year = {2007}
}
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6 pages