We compute the Čech homotopy groups of the m-dimensional infinite earring space \(\mathbb {E}_m\) , i.e. a shrinking wedge of m-spheres. In particular, for all \(n,m\geqslant 2\) , we prove that \(\check{\pi }_n(\mathbb {E}_m)\) is isomorphic to a direct sum of countable powers of homotopy groups of spheres: \(\bigoplus _{1\leqslant j\leqslant \frac{n-1}{m-1}}\left( \pi _{n}(S^{mj-j+1})\right) ^{\mathbb {N}}\) . Equipped with this isomorphism and infinite-sum algebra, we also construct new elements of \(\pi _n(\mathbb {E}_m)\) with a view toward characterizing the image of the canonical homomorphism \(\Psi _{n}:\pi _n(\mathbb {E}_m)\rightarrow \check{\pi }_{n}(\mathbb {E}_m)\) . We prove that \(\Psi _{n}\) is a split epimorphism when \(n\leqslant 2m-1\) and we identify a candidate for the image of \(\Psi _n\) when \(n>2m-1\) .
