Author Archives: Jeremy Brazas

Shape injectivity of the earring space (Part I)

One of my posts where I did some substantial hand-waving is my original post on the fundamental group of the earring space. I wrote about how to understand and work with this group, but I never gave a proof of … Continue reading

Posted in earring space, Free groups, Fundamental group, Inverse Limit, Shape homotopy group, Shape theory, Tree | Tagged , , , , , | 9 Comments

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

Celebrating the Career and Contributions of Katsuya Eda: Master of the Earring Group

Last week, I had the pleasure of speaking at the Arches Topology Conference in Moab, Utah. The conference was in honor of the career and contributions of Katsuya Eda, who retired not too long ago. K. Eda considers himself a … Continue reading

Posted in Algebraic Topology, Conferences, earring space, Fundamental group, Singular homology | Leave a comment