6 problems

Let $M$ be an oriented closed manifold of dimension $n$. Let $C^{\mathrm{sing}}(\Loop_{\Sph{1}}M;\R)$ be the smooth singular chain complex with boundary $\Bdd$, and let…

Let $M$ be a closed oriented manifold of dimension $n$, and let \H_{\mathrm{dR}} be its de Rham cohomology. Let \DBCyc\,\H_{\mathrm{dR}}[2-n] denote a suitable shifted cyclic c…

Let $M$ be a connected, oriented, closed Riemannian manifold with $\HDR^1(M)=0$, and suppose that $M$ is formal. In the situation of the equivalence conjecture, let $\PMC$ be the C…

Let $M$ be a connected, oriented, closed Riemannian $n$-manifold with $\HDR^1(M)=0$. Let $\DR(M)$ be its de Rham complex, $\HDR(M)$ its de Rham cohomology, and…

Let $V$ be a differential Poincaré duality algebra with \H^0(V)=\operatorname{Span}\{1\} and \H^1(V)=0, and suppose that $V$ is formal as a differential graded algebra. A Poinc…

Let $V$ be a differential Poincaré duality algebra with \H^0(V)=\operatorname{Span}\{1\} and \H^1(V)=0, and let $\Model_1$ and $\Model_2$ be Poincaré duality models satisfying…