I would like to have a reference to the following statement which I think is true: $$h^1 \hookrightarrow L^1.$$ The closest I came to this is in D. Goldberg's paper, "A local versi …

Question: What are the connected components of the familiar spaces of functions between two (let's say compact and smooth, for simplicity) manifolds $M$ and $N$? Specifically, I' …