This is more or less the same question as 
[ [What is the generator of $\pi\_9(S^3)$?](https://mathoverflow.net/questions/76899/what-is-the-generator-of-pi-9s3) ], except what I would like to know is if it is possible to describe this map in a way 
not only topologists can make sense of. 


[EDIT] (Following the advice of Ryan Budney.) A purely geometric construction 
like the famous Hopf fibration for $\pi\_3(S^2)$ would be perfect. 
(Something like a map $S^9\to S^2$ or $S^9\to S^3$ which may be written 
down in equations.) But I understand that there is little hope for that. 


A less explicit but probably more reasonable approach is to try and represent this homotopy class by a framed 7-manifold in ${\mathbb R}^9$ following Pontryagin. 
In fact, any information about such a manifold may be of help. Is it really complicated?


I am not really familiar with the work of Jie Wu, but what I have read this far makes sense to me. So, the answer can also be along this lines, but if so I would like to see more then hints. (This computation looks horrendous, and I probably cannot handle it by myself.) 



What is the generator of $\pi_9(S^2)$?
I [posted an answer to the previous question](https://mathoverflow.net/a/332740/1345) describing one way to view a generator of $\pi\_9 S^3$. From the Hopf fibration
$$S^1\to S^3 \overset{\eta}{\to} S^2$$ and fibration long exact sequence,
we know that $$\pi\_9 S^1 = 0 \to \pi\_9 S^3 \overset{\eta}{\to} \pi\_9 S^2\to \pi\_8 S^1=0 $$
is exact, so $\pi\_9 S^3 \cong \pi\_9 S^2$ via the Hopf map $\eta$ (comment made by @skd above). 


I'm not sure if these answers are only understandable by topologists, but all the information is available in Hatcher's book [Algebraic Topology](https://pi.math.cornell.edu/~hatcher/AT/ATpage.html) (however, some of the information is not proved there, e.g. Bott periodicity). 


