See my previous question [here](https://mathoverflow.net/questions/232215/tangent-bundle-of-smooth-closed-simply-connected-4-manifold-w-1-w-2-0-ca).



> 
> Let $M$ be a smooth closed simply-connected $4$-manifold with $w\_1 = w\_2 = 0$. Can $TM$ be trivialized in the complement of a point?
> 
> 
> 


This was answered in the affirmative.


My question now is, is it possible to conclude in some way from Smale's immersion theorem that $M - p$ admits a symplectic structure, where $p$ is a point? I see how to do it with Gromov's $h$-principal, but not with Smale's immersion theorem.



Smooth closed simply-connected $4$-manifold with $w_1 = w_2 = 0$ without a point admits symplectic structure?
By an application of Gromov's $h$-principle, an open manifold $W$ admits a symplectic structure precisely if $TW$ admits an almost complex structure. In the case you are considering it does, as $TW$ is trivial.


