10 problems

Lian–Zuckerman's lifting conjecture. The product and bracket extend to a $G_\infty$ structure on $V$. The conjecture is presented as an open problem in the source, with no resoluti…

Let ${\mathcal A{\it ss}}$ be the associative operad, and let ${\mathcal B}_{{\mathcal A{\it ss}}}$ be the operad of natural operations on the cohomology of associative algebras. L…

Let ${\mathscr{C}}$ be a monoidal category fulfilling a few mild conditions. Let $Z$ be a braided commutative monoid in the left weak monoidal centre of ${\mathscr{C}}$, and let…

Generalized Deligne conjecture. The direct sum

Let $A$ be an associative algebra, and in the cyclic case a cyclic unital associative algebra. Its Hochschild cochain complex has Hochschild cohomology groups carrying a (BV) Gerst…

Cohen's Gerstenhaber structure conjecture. There is an isomorphism of Gerstenhaber algebras

Trivial Lie bracket conjecture. The Lie algebra of this Gerstenhaber algebra is trivial.

Let $M$ be simply connected and let ${\Bbbk}$ be a field. Let $LM=map(S^1,M)$ be the free loop space, let $d$ be the dimension parameter of $M$, and let $S^*(M)$ denote the algebra…

Let $G$ be a topological group such that $M$ is a classifying space of $G$, and let $S_*(G)$ denote the normalized singular-chain algebra of $G$. Write $LM=map(S^1,M)$ for the free…

Let $M$ be a compact oriented $d$-dimensional smooth manifold, let $LM=map(S^1,M)$ be its free loop space, and let $S^*(M)$ denote the differential graded algebra of singular cocha…