Tag Archives: earring space

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 earring group is not free (Part II)

This post is Part II in an explanation of why the fundamental group of the earring space is not a free group. I’ll be referencing the notation and results that we worked through in Part I. Recall that the earring group  is … Continue reading

Posted in earring group, earring space, Free groups, Fundamental group, Group homomorphisms | Tagged , , , , , , | 5 Comments

The earring group is not free (Part I)

The main goal of this two-part post will be to study the homomorphisms out of the earring group. Click here to get to Part II. In particular, we’ll end up concluding that the set of homomorphisms to the additive group … Continue reading

Posted in earring group, earring space, Free groups, Fundamental group, Group homomorphisms | Tagged , , , , , , | 7 Comments