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Let $M$ be a connected, simply connected topological space, and $\pi_2(M)$ its second homotopy group. I am searching for some work/references/papers/... done about such a space with $\pi_2(M)$ which is non-finitely-generated.

Are there some known and interesting results?

Thanks ;-)

Let $M$ be a connected, simply connected topological space, and $\pi_2(M)$ its second homotopy group. I am searching for some work/references/papers/... done about such a space with $\pi_2(M)$ which is non-finitely-generated.

Are there some known and interesting results?

Since the question is very broad, one can take an example: how does a space $M$ with $\pi_2(M)=\mathbb{Q}$ look like?

Thanks ;-)

Let $X$ be a connected, simply connected topological space, and $\pi_2(M)$ its second homotopy group. I am searching for some work/references/papers/... done about such a space with $\pi_2(M)$ which is non-finitely-generated.

Are there some known and interesting results?

Thanks ;-)

Let $M$ be a connected, simply connected topological space, and $\pi_2(M)$ its second homotopy group. I am searching for some work/references/papers/... done about such a space with $\pi_2(M)$ which is non-finitely-generated.

Are there some known and interesting results?

Thanks ;-)