Category Archives: harmonic archipelago

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

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 Hausdorff Spaces (Part II)

In my post homotopically Hausdorff spaces (Part I), I wrote about the property which describes the existence of loops that can be deformed into arbitrarily small neighborhoods but which are not actually null-homotopic, i.e. can’t be deformed all the way back … Continue reading

Posted in Algebraic Topology, Fundamental group, Group homomorphisms, harmonic archipelago, Hawaiian earring | Tagged , , | 2 Comments