Timeline for Manifolds with prescribed fundamental group and finitely many trivial homotopy groups
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 15, 2012 at 6:19 | vote | accept | Mark Bell | ||
| Oct 14, 2012 at 11:52 | comment | added | Misha | @Fernando: The paper is called "Combinatorial Topology, I". Whitehead proves that every countable $n$-dimensional cell complex is homotopy-equivalent to a locally finite one. If one is willing to increase dimension by 1 then there is an easier argument, see the remark by Igor Belegradek in mathoverflow.net/questions/90570/… | |
| Oct 14, 2012 at 10:46 | history | edited | Mark Bell | CC BY-SA 3.0 |
added 25 characters in body
|
| Oct 14, 2012 at 10:45 | comment | added | Mark Bell | Sorry, despite my efforts to make sure I wrote "finitely presented" I ended up writing finitely generated. I'll edit the question. | |
| Oct 14, 2012 at 2:13 | comment | added | John Klein | Doesn't $G$ need to be finitely presented? | |
| Oct 13, 2012 at 15:36 | comment | added | Fernando Muro | @Misha, interesting, what paper of Whitehead is that? thanks! | |
| Oct 13, 2012 at 13:14 | answer | added | Johannes Ebert | timeline score: 17 | |
| Oct 13, 2012 at 3:22 | comment | added | Misha | @Fernando: This is nota problem, you deform this complex to a locally finite one (proven by Whitehead in 1947), which then admits a proper embedding in Euclidean space. | |
| Oct 12, 2012 at 22:10 | comment | added | Fernando Muro | When you start killing homotopy groups you may need to attach infinitely-many new cell in each step, even if $G$ is finitely presented. As a consequence of this, you may not be able to embed the resulting CW-complex in an euclidean space of any dimension. | |
| Oct 12, 2012 at 21:42 | history | asked | Mark Bell | CC BY-SA 3.0 |