All Questions

Let $X$ be a polyhedron. For each $n$-dimensional face $f$ of $X$ fix a homeomorphism $\sigma_f:\triangle^n\to f$ where $\triangle^n$ is the standard $n-$simplex so that whenever $f$ is a face of $f'$ ...

For simplicity let me work only with connected and simply connected spaces. "Space" will mean a space of this type. A space is rational if its homotopy groups are rational vector spaces (...

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 ...

I don't know if this question is elementary or not. Suppose we have a rationalization $X_\mathbb{Q}$ of a simply connected topological space $X$. Then we can construct a CDG-algebra - a minimal ...

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 ...