Category Archives: Group theory

Infinite Commutativity (Part II)

Posted on August 3, 2020 by Jeremy Brazas

In Infinite Commutativity: Part I, I described infinite commutativity in general terms with some basic examples, including real infinite series. In this post, I’ll discuss how the homotopy groups , are more than just abelian in the ordinary sense. Their … Continue reading →

Posted in Algebraic Topology, Higher Homotopy groups, Homotopy theory, Infinite Group Theory, Infinite products | 3 Comments

Infinite Commutativity (Part I)

Posted on August 2, 2020 by Jeremy Brazas

The Eckmann-Hilton Principle is a classical argument in algebraic topology/algebra. This argument allows you to conclude that an operation which may be expressed in two different ways (imagine that it may be applied both horizontally and vertically when written) is … Continue reading →

Posted in Baer-Specker group, Homotopy theory, Infinite Group Theory, Infinite products | Tagged , , , , , , | 1 Comment

Shape injectivity of the earring space (Part II)

Posted on August 6, 2019 by Jeremy Brazas

This is the sequel to Shape injectivity of the earring space (Part I) We’re on our way to proving the canonical homomorphism from the earring group to the inverse limit of free groups is injective. Part I was mostly dedicated … Continue reading →

Posted in Dendrite, earring group, earring space, Free groups, Fundamental group, Inverse Limit, Peano continuum, Shape theory, Tree | 3 Comments