Tag Archives: homomorphism

Homomorphisms from the harmonic archipelago group to finite groups

Posted on June 8, 2014 by Jeremy Brazas

This post is a brief application of a result discussed in the last post about the existence of odd ways to map the fundamental group of the Hawaiian earring onto an arbitrary finite group : Theorem 1: Let be any non-trivial finite group and be a loop … Continue reading →

Posted in Cardinality, Finite groups, Fundamental group, harmonic archipelago | Tagged , , , , , | Leave a comment

Homomorphisms from the earring group to finite groups

Posted on June 7, 2014 by Jeremy Brazas

One of the the surprising things about the earring group (the fundamental group of the earring space ) is that the group of homomorphisms to the additive group of integers is countable (see this post for details) even though is … Continue reading →

Posted in earring group, earring space, Finite groups, Fundamental group, Group homomorphisms, Ultrafilter | Tagged , , , , , , , , , , , , | 1 Comment

The Harmonic Archipelago Group is not Free

Posted on May 18, 2014 by Jeremy Brazas

In recent posts, I’ve been writing about the behavior of fundamental groups of the most fundamental “wild” spaces. We did a decent amount of work in a two-part post to convince ourselves that the fundamental group of the earring space … Continue reading →

Posted in earring group, earring space, Free groups, Fundamental group, Group homomorphisms, harmonic archipelago | Tagged , , , , , , , , | 2 Comments