Category Archives: Higher Homotopy groups

Visualizing the Hopf Fibration

Posted on August 21, 2021 by Patrick Gillespie

This is a guest post by Patrick Gillespie, who is currently a 2nd year Ph.D. student at the University of Tennessee Knoxville. The Hopf map is a classical example of a non-trivial fiber bundle. There are many great visualizations of … Continue reading →

Posted in Algebraic Topology, Higher Homotopy groups, 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