Timeline for cohomology ring of mapping spaces
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 14, 2015 at 12:07 | comment | added | Pax | I'll just list some basics. Since the mapping space is only dependent on the based homotopy class of $M$, $M=\mathbb{R}^n$ is trivial. For $M=S^{1}\times \mathbb{R}$, then $Map_*(S^1, S^n)=\Omega S^n$, so the cohomology is $\mathbb{Z}/(2)$ in degrees divisible by $n$, and $0$ otherwise. The case of higher tori gets extremely complicated, see here, but the Serre spectral sequence associated to $Map(\mathbb{T}^{m}, S^n)\to *\to Map(\mathbb{T}^{m-1}, S^n)$ can, for example, that for $m=2$ and $n=2s+1$, it is a polynomial ring. | |
| Jul 14, 2015 at 9:27 | history | edited | QSR | CC BY-SA 3.0 |
added 9 characters in body
|
| Jul 14, 2015 at 8:36 | history | edited | QSR | CC BY-SA 3.0 |
added 303 characters in body
|
| Jul 14, 2015 at 8:28 | history | asked | QSR | CC BY-SA 3.0 |