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We examine topological properties of pointed metric measure spaces $(Y, p)$that can be realized as the pointed Gromov-Hausdorff limit of a sequence ofcomplete, Riemannian manifolds $\{(M^n_i, p_i)\}_{i=1}^{\infty}$ withnonnegative Ricci curvature. Cheeger and Colding \cite{ChCoI} showed that givensuch a sequence of Riemannian manifolds it is possible to define a measure$\nu$ on the limit space $(Y, p)$. In the current work, we generalize previousresults of the author to examine the relationship between the topology of $(Y,p)$ and the volume growth of $\nu$. In particular, we prove a Abresch-Gromolltype excess estimate for triangles formed by limiting geodesics in the limitspace. Assuming explicit volume growth lower bounds in the limit, we show thatif $\lim_{r \to \infty} \frac{\nu(B_p(r))}{\omega_n r^n} > \alpha(k,n)$, thenthe $k$-th group of $(Y,p)$ is trivial. The constants $\alpha(k,n)$ areexplicit and depend only on $n$, the dimension of the manifolds $\{(M^n_i,p_i)\}$, and $k$, the dimension of the homotopy in $(Y,p)$.

Volume growth and the topology of Gromov-Hausdorff limits