Monthly Archives: May 2014

The earring group is not free (Part I)

The main goal of this two-part post will be to study the homomorphisms out of the earring group. Click here to get to Part II. In particular, we’ll end up concluding that the set of homomorphisms to the additive group … Continue reading

Posted in earring group, earring space, Free groups, Fundamental group, Group homomorphisms | Tagged , , , , , , | 7 Comments

The Harmonic Archipelago

Another fascinating space that receives a lot of attention is the so-called harmonic archipelago which is the following subspace of . You can describe the construction like this: Start by drawing the usual earring space onto a solid disk in … Continue reading

Posted in Algebraic Topology, earring space, Fundamental group, harmonic archipelago | Tagged , , , , , | 11 Comments