Category Archives: Infinite products

The Griffiths twin cone and the harmonic archipelago have isomorphic fundamental group (Part 2)

This is Part 2 of a guest post by Sam Corson, who is a Heibronn Fellow at the University of Bristol. It will be helpful to read Part 1 first. We will furthermore overload the notation used for word concatenation … Continue reading

Posted in Fundamental group, Griffiths twin cone, harmonic archipelago, Infinite Group Theory, Infinite products, Order Theory | Tagged , , | Leave a comment

Infinite Commutativity (Part II)

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)

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