Category Archives: Griffiths twin cone

Topologized Fundamental Groups: The Quotient Topology Part 4 (Subgroup Classifications)

Posted on October 7, 2023 by Jeremy Brazas

This is the last in a sequence of posts about the quotient topology. This one is about how the topological structure of can be used to classify certain generalizations of covering maps for locally complicated spaces. Sometimes it still amazes … Continue reading →

Posted in Algebraic Topology, core of a subgroup, Fundamental group, Generalized covering space theory, Griffiths twin cone, harmonic archipelago, Quasitopological groups, quotient topology, semicovering, topological fundamental group, Uncategorized | 7 Comments

The Griffiths twin cone and the harmonic archipelago have isomorphic fundamental group (Part 2)

Posted on June 14, 2021 by topologyandgrouptheory

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)

Posted on June 7, 2021 by topologyandgrouptheory

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