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Category Archives: Homotopy theory
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
Homotopically Reduced Paths (Part III)
In this last post about reduced paths, I’m going to work through the details of one of the most useful results in wild topology. Writing this post helped me work out my own way of proving this result and hopefully … Continue reading
Homotopically Reduced Paths (Part II)
Understanding this post requires reading Part I where I explain what reduced paths are and how we might go about proving they exist. In this second part, I’ll go into detail about how to use Zorn’s lemma to identifying a … Continue reading