I should mention I have very little background in algebraic topology and don't really know much about homotopy groups besides the definition.
I am aware that for a topological space $X$ and a point $x \in X$ the fundamental group $\pi_1(X,x)$ acts on all homotopy groups $\pi_n(X,x)$. In particular, this means the $\mathbf{Q}$-vector space $\mathbf{Q} \otimes_\mathbf{Z}\pi_n(X,x)$ is endowed with a linear action by $\pi_1(X,x)$ and hence defines a local system of $\mathbf{Q}$-vector spaces on $X$. If $X$ is a (complex) manifold or something and one can appeal to tools akin to the Riemann-Hilbert correspondence and other interpretations of these objects, can one describe these explicitly? Are they 'tautological' local systems in some sense... ? Can anything be said about the family of local systems $(\mathbf{Q}\otimes_\mathbf{Z}\pi_n(X,x))_{n \geq 2}$ and can these be recognised as something else?
I'm not sure my question makes much sense and I was just trying to satiate a curiosity :) Any words of wisdom are appreciated and thank you very much! :D
Edit: moved to MO