Tag Archives: torsion free

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 fundamental group of the earring space

Here is one of my favorite spaces: The earring space, i.e. the “shrinking wedge of circles.” This space is the first step into the world of “wild” topological spaces. This post is meant to be an introduction into how one … Continue reading

Posted in Algebraic Topology, earring group, earring space, Fundamental group, Homotopy theory | Tagged , , , , , , | 20 Comments