Category Archives: Shape theory

Shape injectivity of the earring space (Part II)

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

Shape injectivity of the earring space (Part I)

One of my posts where I did some substantial hand-waving is my original post on the fundamental group of the earring space. I wrote about how to understand and work with this group, but I never gave a proof of … Continue reading

Posted in earring space, Free groups, Fundamental group, Inverse Limit, Shape homotopy group, Shape theory, Tree | Tagged , , , , , | 8 Comments

The Cech Expansion: nerves of open covers

The Whitehead theorem in homotopy theory basically says that to fully understand the homotopy type of a CW-complex one only needs to know about the homotopy groups (really, the weak homotopy type). It is very easy to produce spaces to … Continue reading

Posted in Cech expansion, Shape theory, Simplicial complexes | Tagged , , , , , | 4 Comments