Timeline for Algebraic models of non-simply connected spaces in string topology
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 3, 2018 at 22:33 | comment | added | mme | For the special case of the torus $T^n$, the fibration $\Omega T^n \to LT^n \to T^n$ is trivial: the fiber is contractible to $\Bbb Z^n$, so $LT^n$ is homotopy equivalent to a covering space, and each element of the fiber belongs to a distinct component of $LT^n$ (this uses that $\Bbb Z^n$ is an abelian group, so every conjugacy class is one element), so the covering space is trivial. So $LT^n \simeq \Bbb Z^n \times T^n$. I imagine the $\text{Diff}(S^1)$-equivariant homotopy type is more complicated. | |
| Aug 3, 2018 at 20:23 | vote | accept | Yining Zhang | ||
| Aug 3, 2018 at 20:00 | answer | added | Manuel Rivera | timeline score: 11 | |
| Aug 3, 2018 at 15:35 | history | asked | Yining Zhang | CC BY-SA 4.0 |