Timeline for Manifolds with prescribed fundamental group and finitely many trivial homotopy groups
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 15, 2012 at 6:19 | vote | accept | Mark Bell | ||
| Oct 13, 2012 at 23:33 | comment | added | Fernando Muro | Ah, I see, ok, ok. | |
| Oct 13, 2012 at 23:31 | comment | added | Johannes Ebert | @Fernando: I meant that I could embed a skeleton of $BG$, not all of it. | |
| Oct 13, 2012 at 22:38 | comment | added | Fernando Muro | No way if $BG$ has infinite cohomological dimension. | |
| Oct 13, 2012 at 17:45 | comment | added | Johannes Ebert | The (now deleted) answer answered a different question, namely if one could have a noncompact manifold without boundary. That is certainly true and not so difficult: if $G$ is countable, then the standard $BG$ has countable skeleta that can be deformed and embedded into some $R^k$ as in Mishas comment. Take an open neighborhood. | |
| Oct 13, 2012 at 13:32 | comment | added | Donu Arapura | It's always awkward when answers reach different conclusions, but I am convinced by this. I guess one could (almost) rephrase the first part by saying that if the group has infinitely generated homology in some degree $< n$, then no such compact manifold can exist. | |
| Oct 13, 2012 at 13:14 | history | answered | Johannes Ebert | CC BY-SA 3.0 |