Category Archives: Homotopy theory

Testing the limits of Eda’s Theorem

Posted on October 18, 2020 by Jeremy Brazas

With everything going on, it’s been a bit tough to find time to post about the things I’d like to. I’ve promised posts about topological homotopy groups for a while but I want to do those right, so it may … Continue reading →

Posted in earring group, earring space, Fundamental group, Homotopy theory | Tagged , , , | Leave a comment

Infinite Commutativity (Part II)

Posted on August 3, 2020 by Jeremy Brazas

In Infinite Commutativity: Part I, I described infinite commutativity in general terms with some basic examples, including real infinite series. In this post, I’ll discuss how the homotopy groups , are more than just abelian in the ordinary sense. Their … Continue reading →

Posted in Algebraic Topology, Higher Homotopy groups, Homotopy theory, Infinite Group Theory, Infinite products | 3 Comments

Infinite Commutativity (Part I)

Posted on August 2, 2020 by Jeremy Brazas

The Eckmann-Hilton Principle is a classical argument in algebraic topology/algebra. This argument allows you to conclude that an operation which may be expressed in two different ways (imagine that it may be applied both horizontally and vertically when written) is … Continue reading →

Posted in Baer-Specker group, Homotopy theory, Infinite Group Theory, Infinite products | Tagged , , , , , , | 1 Comment