6 problems

Combined injectivity conjecture. For odd $k$ and $n>1$, the direct-sum map

Chain-homotopy conjecture. The maps $g_1^j$ and $g_2^j$ are chain homotopic. The source notes that these maps are chain maps for the stated prime orders; proving their chain homoto…

Let $p$ be an odd prime, and let $\operatorname{R}_p$ be the dihedral quandle of order $p$. Write $\operatorname{H}^{\rm R}_n(\operatorname{R}_p)$ for its rack homology. Fenn–Rourk…

Let $R_{(m)}$ be the rack considered in the paper, let $H_3(R_{(m)})$ denote its third Yang–Baxter homology over $k$, and let $m$ be the parameter indexing this rack family. The th…

The Homflypt Yang–Baxter homology conjecture. For $m=2$, one has

An associative shelf is a set equipped with an associative, self-distributive binary operation. Its two-term (rack) homology groups are the homology groups obtained from the associ…