Timeline for When is a classifying space a topological manifold?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 22, 2012 at 4:26 | comment | added | Misha | Yes, but the construction is not very explicit. All I could tell you is that the manifold will have dimension $\le 6$ (you can get it down to $4$ if Eilenberg-Ganea conjecture holds for this group). | |
| Mar 21, 2012 at 16:26 | comment | added | yeshengkui | That's interesting. Do you mean for the rationals $Q$ we can find a manifold whose fundamental group is $Q$? | |
| Mar 11, 2012 at 23:44 | comment | added | Misha | Igor Belegradek has found a very nice modern reference for Whitehead's result on the last page of math.cornell.edu/~hatcher/AT/AT-exercises.pdf This is given as an exercise with a hint and the proof (via a mapping telescope) is much easier and nicer than the original one. | |
| Mar 9, 2012 at 2:00 | comment | added | Misha | The proof I gave is well-known (among topologists) provided that $G$ admits $K(G,1)$ which is a finite CW-complex. The only tricky issue in general is to get local finiteness for which the only reference I know is the original Whitehead's paper. Does somebody know a modern reference? | |
| Mar 9, 2012 at 1:46 | comment | added | Misha | Hausdorff, 2nd countable, locally homeomorphic to ${\mathbb R}^n$. | |
| Mar 9, 2012 at 1:37 | comment | added | Greg Friedman | What do you mean by "(textbook) topological manifold"? | |
| Mar 8, 2012 at 21:07 | vote | accept | berl13 | ||
| Mar 8, 2012 at 19:20 | history | answered | Misha | CC BY-SA 3.0 |