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Category Archives: Higher Homotopy groups
Topologized Fundamental Groups: The Whisker Topology, Part 3
In Part 1 and Part 2, I gave detailed introductory exposition about the whisker topology on the fundamental group. In general, this topologized fundamental group is a left topological group and therefore a homogeneous space. Moreover, whenever this group is … Continue reading
Visualizing the Hopf Fibration
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 nontrivial fiber bundle. There are many great visualizations of … Continue reading
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