7 problems

Cyclic cohomology conjecture. The cyclic cohomology of $(H,R)$ satisfies

Cyclic cohomology conjecture. The cyclic cohomology of $A^{\infty}$ is given by

Let $A^{\infty}$ be the smooth subalgebra of the group $C^*$-algebra associated with the dihedral group, and let $HC^n(A^{\infty})$ denote its cyclic cohomology in degree $n$. Cycl…

Loday's proposal. These data should satisfy

Non-triviality conjecture. The cyclic cohomology class $[\mathfrak{c}_\omega]$ and the associated Hochschild cohomology class $[\mathfrak{h}_\omega]$ are non-trivial. These classes…

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…

Kontsevich's cyclic formality conjecture. For each volume form $\Omega\in\Omega^d(M)$ there exists an $L_\infty$-quasi-isomorphism of $L_\infty$-algebras