Let X be an affine variety over ℂ. Consider X(ℂ) with the classical topology, and create the topologists loop space ΩX(ℂ) of maps from the circle into X(&#8 …

There are two ways to define smooth mapping spaces and I want to know how they compare? Let's take the concrete special case of free loops spaces. I think this is the most studied …

One could try to apply the Eilenberg-Moore spectral sequence to the pullback diagram • → X ← •, obtaining a spectral sequence TorH•(X, R)(R, R) => H•( …