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For ''n'' > 2, however, proving the impossibility of the retraction is more difficult. One way is to make use of [[Homology (mathematics)|homology groups]]: the homology ''H''<sub>''n''−1</sub>(''D''<sup>''n''</sup>) is trivial, while ''H''<sub>''n''−1</sub>(''S''<sup>''n''−1</sup>) is infinite [[cyclic group|cyclic]]. This shows that the retraction is impossible, because again the retraction would induce an injective group homomorphism from the latter to the former group.
The impossibility of a retraction can also be shown using the [[de Rham cohomology]] of open subsets of Euclidean space ''E''<sup>''n''</sup>. For ''n'' ≥ 2, the de Rham cohomology of ''U'' = ''E''<sup>''n''</sup> – (0) is one-dimensional in degree 0 and ''n''
===A proof using Stokes' theorem===
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