Tag Archives: harmonic archipelago

The Harmonic Archipelago Group is not Free

In recent posts, I’ve been writing about the behavior of fundamental groups of the most fundamental “wild” spaces. We did a decent amount of work in a two-part post to convince ourselves that the fundamental group of the earring space … Continue reading

Posted in earring group, earring space, Free groups, Fundamental group, Group homomorphisms, harmonic archipelago | Tagged , , , , , , , , | 2 Comments

The Harmonic Archipelago

Another fascinating space that receives a lot of attention is the so-called harmonic archipelago which is the following subspace of . You can describe the construction like this: Start by drawing the usual earring space onto a solid disk in … Continue reading

Posted in Algebraic Topology, earring space, Fundamental group, harmonic archipelago | Tagged , , , , , | 10 Comments