Timeline for Are there any tests for knowing whether a topological space admits a CW structure?
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 4 at 9:38 | vote | accept | Tyrannosaurus | ||
| Dec 3 at 5:24 | comment | added | Moishe Kohan | Kirby and Sibenmann did not know this (when they wrote their book) but also every topological 5-manifold (compact or not) admits a handlebody decomposition, hence, a CW complex structure. This is the main theorem in section 9.1 of the book by Freedman and Quinn. | |
| Dec 2 at 14:39 | comment | added | Wojowu | @ToddTrimble Missed it, thank you | |
| Dec 2 at 14:37 | comment | added | Todd Trimble | @Wojowu A comment by Igor Belegradek below the linked MO answer says that the dim $\geq 6$ result is given on p. 107 of Kirby-Siebenmann. | |
| Dec 2 at 14:32 | comment | added | Anthony Conway | References can be found in the proofs of Theorems 3.13 and 3.16 of this very helpful survey: arxiv.org/pdf/1910.07372 | |
| Dec 2 at 11:21 | comment | added | Wojowu | I don't see how the result of the first paragraph precludes existence of a (homotopy-invariant) invariant for a CW structure. It may be that the obstruction is only applicable for spaces which are closed manifolds. So unless we have that any closed manifold has homotopy type of a CW complex which is also a closed manifold, I fail to see the conclusion. | |
| Dec 2 at 11:18 | comment | added | Wojowu | Neither the paper nor the MO post you link seem to mention the $\dim\geq 6$ result you mention. Would you happen to have a reference for it? | |
| Dec 2 at 10:39 | history | edited | Francesco Polizzi | CC BY-SA 4.0 |
deleted 42 characters in body
|
| Dec 2 at 10:12 | history | edited | Francesco Polizzi | CC BY-SA 4.0 |
added 71 characters in body
|
| Dec 2 at 10:06 | history | answered | Francesco Polizzi | CC BY-SA 4.0 |