Category Archives: Fundamental group

The Griffiths twin cone and the harmonic archipelago have isomorphic fundamental group (Part 1)

This is a guest post by Sam Corson, who is a Heibronn Fellow at the University of Bristol. This first post will provide background on the infinite word combinatorics which are used in the description of the fundamental group of … Continue reading

Posted in Fundamental group, Griffiths twin cone, Group theory, harmonic archipelago, Infinite Group Theory | Tagged | 2 Comments

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

Posted in Algebraic Topology, Dendrite, Fundamental group, Fundamental groupoid, Homotopy theory, Inverse Limit, one-dimensional spaces, reduced paths | Leave a comment

Homotopically Reduced Paths (Part I)

The topic of this post focuses on a general concept that is heavily used in the wild topology world. Writing this post has been a fun exploration I’ve been meaning to spend time on for a while now. I will … Continue reading

Posted in Fundamental group, Homotopy theory | Tagged , | 2 Comments