Tag Archives: free group

What is an infinite word?

In this post, we’ll explore the idea of non-commutative infinitary operations on groups, that is, multiplying together infinitely many elements in a group. This idea arises very naturally in “wild” or “infinitary” algebraic topology. In fact, lately, this has been … Continue reading

Posted in Group theory, Infinite Group Theory, Order Theory | 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 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 Free groups, Fundamental group, Hawaiian earring | Tagged , , , , , | 5 Comments