We can join two $S^d$'s via a connected sum to obtain $S^d\#S^d=S^d$. We can also deform a single $S^d$ via a self-connected sum (ie add a handle) to obtain $\#_\text{self}S^d=S^{d-1}\times S^1$.

When $d=2$, the self-connected sums can generate all 2-dimensional closed oriented manifolds from $S^2$. Do we have a similar result for higher dimensions? ie can all d-dimensional closed orientable manifolds be constructed via connected sums and self-connected sums from many $S^d$'s?

If the answer is no, then we may replace connected sum by fiber sum: can all d-dimensional closed orientable manifolds be constructed via fiber sums and self-fiber sums from many $S^d$'s?

We can join two $S^d$'s via a connected sum to obtain $S^d\#S^d=S^d$. We can also deform a single $S^d$ via a self-connected sum (ie add a handle) to obtain $\#_\text{self}S^d=S^{d-1}\times S^1$.

When $d=2$, the self-connected sums can generate all 2-dimensional closed oriented manifolds from $S^2$. Do we have a similar result for higher dimensions? ie can all d-dimensional closed orientable manifolds be constructed via connected sums and self-connected sums from many $S^d$'s?

If the answer is no, then we may replace connected sum by fiber sum: can all d-dimensional closed orientable manifolds be constructed via fiber sums and self-fiber sums from many $S^d$'s?

Although I asked the question in terms of manifold, here I do not require the manifold to be smooth. In other words,we may replace the term "manifold" in the above by CW complex.

We can join two $S^d$'s via a connected sum to obtain $S^d\#S^d=S^d$. We can also deform a single $S^d$ via a self-connected sum (ie add a handle) to obtain $\#_\text{self}S^d=S^{d-1}\times S^1$.

When $d=2$, the self-connected sums can generate all 2d closed oriented manifolds from $S^2$. Do we have a similar result for higher dimensions? ie can all d-dimensional closed orientable manifolds be constructed via connected sums and self-connected sums from many $S^d$'s?

If the answer is no, then we may replace connected sum by fiber sum: can all d-dimensional closed orientable manifolds be constructed via fiber sums and self-fiber sums from many $S^d$'s?

We can join two $S^d$'s via a connected sum to obtain $S^d\#S^d=S^d$. We can also deform a single $S^d$ via a self-connected sum (ie add a handle) to obtain $\#_\text{self}S^d=S^{d-1}\times S^1$.

When $d=2$, the self-connected sums can generate all 2-dimensional closed oriented manifolds from $S^2$. Do we have a similar result for higher dimensions? ie can all d-dimensional closed orientable manifolds be constructed via connected sums and self-connected sums from many $S^d$'s?

If the answer is no, then we may replace connected sum by fiber sum: can all d-dimensional closed orientable manifolds be constructed via fiber sums and self-fiber sums from many $S^d$'s?