11 problems

Let $V$ be a topological vertex operator algebra, and let an appropriate topological completion mean the completion of $V$ required in the cited construction. A genus-zero topologi…

A topological vertex operator algebra is the algebraic structure considered in the paper, and a homotopy Gerstenhaber algebra is the corresponding higher-algebraic structure introd…

Let a homology group carry the structure of an involutive Lie bialgebra, a particular type of Lie bialgebra. Lifting conjecture. This structure can be lifted to a structure of an i…

Let $B^{{\bullet}{\bullet}}(m,n)$ be the bicomplex associated with the compactified configuration spaces $\overline{K(m,n)}$, and let $D$ denote its differential. For each graph…

The transferred operations $\nu$, $\varphi$, $\psi$, and $H$ are sums of monomials in the initial data $\mu_2,\mu_3,\ldots,f,g,h$, with coefficients $\pm1$. Let $K_n$, $n\geq2$, be…

Let $X$ be a smooth curve and let $M$ be a chiral algebra on $X$. Its deformations are controlled by a differential graded pro-$*$-Lie algebra $\mathfrak g$. A coisson algebra is a…

Let $\widehat{W}_N$ be the graded vector space generated by cyclic words in the letters $\{x_1[-p],\ldots,x_N[-p]\}_{p\in\mathbb{N}}$, and let … be the explicitly constructed stron…

Koszulity conjecture. The constant operad

Let $A$ be an $\mathrm{E}_1$-algebra, and let its deformation complex be the bar construction associated to its $\mathcal{As}_\infty$-algebra structure. The $\mathrm{E}_1$-version…

Let $M$ be a smooth $n$-dimensional manifold, let $LM$ be its free loop space, and let $C_*^{S^1}(LM)$ be the complex of $S^1$-equivariant chains, where $S^1$ acts on loops by repa…

Homotopy-lifting conjecture. All secondary constructions come from suitable homotopy structures at the level of characteristic cochains.