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Jan 18, 2016 at 19:04 comment added Matthias Ludewig A map to the loop space is smooth if and only if it maps smooth curves to smooth curves. A smooth curve in the Loop space over $S^n$ is just a map from a cylinder to $S^n$ (plus some base condition if you want). This should give you enough tools to verify the statement.
Jan 18, 2016 at 16:12 history edited Aloizio Macedo CC BY-SA 3.0
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Jan 17, 2016 at 15:19 history asked Aloizio Macedo CC BY-SA 3.0