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In 1926 Kneser showed that homeomorphisms of $ \mathbf{S}^2$ admit a retraction into the orthogonal group $ O(3)$ . Smale extended this result to Diffeomorphisms of $ \mathbf{S}^2$ in 1958; however, in that paper he assumes that the diffeomorphisms are of class $ C^k$ for $ k\geq 2$ . So my question is: Has anyoneRead more