Tag Archives: integers

Homomorphisms from the earring group to finite groups

One of the the surprising things about the earring group (the fundamental group of the earring space ) is that the group of homomorphisms to the additive group of integers is countable (see this post for details) even though is … Continue reading

Posted in Finite groups, Fundamental group, Hawaiian earring, Ultrafilter | Tagged , , , , , , , , , , , , | 1 Comment

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 Free groups, Fundamental group, harmonic archipelago, Hawaiian earring | Tagged , , , , , , , | 2 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 Free groups, Fundamental group, Group homomorphisms, Hawaiian earring | Tagged , , , , , | 7 Comments