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The fundamental group of the harmonic archipelago

Paul Fabel
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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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Paul Fabel. 2005-01-24. The fundamental group of the harmonic archipelago. https://arxiv.org/abs/math/0501426

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