Hi all,

I suspect this is basic stuff, and could be sussed out from something that you all have written (perhaps Urs’ big book), but if I have a manifold $M$ is there an object, I’ll call it $X$ for now, such that (some version of) maps from $M$ to $X$ classify twists of de Rham cohomology on $M$? In other words, the trivial map should just give us regular de Rham cohomology, and non-trivial maps should give us twists. I’m thinking in analogy with a map $Y\to Pic(R)$, where $R$ is a ring spectrum, giving me twists of $R$-homology of $Y$.

Apologies if this is very basic, or perhaps nonsensical.

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