9 problems

Noncommutativity conjecture. The homology bialgebra of the dual of ${\mathcal {T}_*\mathcal{D}}^{odd}$ is not commutative for some ring of coefficients.

Let $v_3^1$ be the cocycle over the integers associated with the first non-trivial $1$-cocycle of the space of long knots. For knots $k_1$, $k_2$, and $k$, let $[k_1,k_2]$,…

Let $A$ be the complex of bracket star-diagrams, with its differential bialgebra structure, and let $H_*(\mathcal K)$ denote the homology bialgebra of the space $\mathcal K$ of lon…

Let $d$ be the ambient dimension, let $A$ be the complex of bracket star-diagrams equipped with the differential bialgebra structure constructed in the paper, and let…

Let $\sigma$ be the simplicial resolution of the discriminant $\Sigma$ of the space of long knots, and let … be its natural filtration. Write $\bar\sigma_i$ and $\bar\sigma$ for th…

Vassiliev's stabilization conjecture. The spectral sequence associated with this filtration and computing the Borel–Moore homology groups of the resolution $\sigma$ stabilizes over…

Let $H_{d,\text{far}}^i$ denote the submodule of $i$-th cohomology classes in degree $d$ represented by cocycles in the far subcomplex, and let $H^i(\mathcal{K}\setminus\Sigma)$ be…

Let $R$ denote the radius of convergence of the Poincaré series of the space of long knots modulo immersions. Positive-radius conjecture. The radius of convergence is positive; tha…

Let $\overline{\operatorname{Emb}}_c(\mathbb{R}^m,\mathbb{R}^n)$ denote the homotopy fibre of the inclusion of embeddings into immersions, and let $\pi_*^{(t-\ell,t)}$ denote its c…