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I'm a grad student studying non-negative curvature on simply-connected manifolds and the conjectured relationship with rational homotopy theory. The rational homotopy groups (and so the number of ...

Let $M$ be a smooth manifold, and let $\Omega^\bullet(M)$ be the commutative dg-algebra of differential forms on $M$. It is quasi-isomorphic to the dg-algebra of singular cochains on $M$. If $M$ is no ...