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Tag Archives: free group
What is an infinite word?
In this post, we’ll explore the idea of noncommutative 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
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 twopart post to convince ourselves that the fundamental group of the earring space … Continue reading
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