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In rational homotopy theory, one can study the rational homotopy and cohomology categories via an algebraic structure, respectively the rational Lie Algebra model and the Sullivan cdga model. If I am ...

Let $K$ be an algebraically closed field and $G$ a group. Given a dg-algebra $A$, a left $A$-module $M$ and a right $A$-module $N$ let $Tor_A(M,N)$ denote the homology of the derived tensor product $M ...

Let $M$ be a simply connected closed Riemannian manifold. How does one find a necessary condition going both ways that may be imposed on $M$ (perhaps on the curvature of $M$ and on torsion) which ...

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 ...