Timeline for Which homology classes from loop space?
Current License: CC BY-SA 3.0
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| Nov 28, 2014 at 18:47 | comment | added | Lennart Meier | Is should be equivalent to ask: What elements in $H_2(Q)$ can be represented by maps $f:M\to Q$ from a surface such that $Im(\pi_0(Lf))\subset S$. A simpler version might replace $\pi_0(LQ)$ by $H_1(Q)$. As degree $1$-maps are surjective in homology, you can only represent $[Q]\in H_2(Q)$ by a map $f: M\to Q$ if $f$ is surjective on $H_1$. It should be possible to solve the $H_1$-question for all surfaces completely. | |
| Nov 28, 2014 at 16:57 | history | asked | Frol Zapolsky | CC BY-SA 3.0 |