The fundamental group of the harmonic archipelago

Details The fundamental group of the harmonic archipelago The fundamental group of the harmonic archipelago

2005-01-24

arxiv.org/abs/math/0501426v1

Mathematics

Algebraic Topology

6 pages

Scientific paper

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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