7 problems

Non-embeddability conjecture. The complex $L$ does not embed in $\mathbb{R}^{2d}$. This generalizes the example discussed in the source and is described there as joint work in prog…

Generalized Menger embedding conjecture. The van Kampen obstruction of $K\times L$ is non-zero.

Let $K$ and $L$ be simplicial complexes, and let $\vartheta$ denote their van Kampen obstruction. Algebraic Menger conjecture. If … then … This is presented as a second algebraic n…

Let $K$ and $L$ be simplicial complexes, and let $\vartheta$ denote their van Kampen obstruction. Algebraic Grünbaum–van Kampen–Flores conjecture. If … then … The conjecture is an…

Van Kampen obstruction conjecture. The van Kampen obstruction vanishes if and only if $\varphi$ is approximable by embeddings.

Let $L$ be a simplicial complex, let $l$ be an integer with $H_l(L;\mathbb{Z}/2)\neq 0$, let $M\in Z_l(L;\mathbb{Z}/2)$ be an $l$-cycle, and let $\Delta$ be a simplex in $M$. The p…

Let $K$ be a $d$-dimensional balanced complex, and let $\mathfrak{o}(K)$ denote its van Kampen obstruction to PL embeddability in $\mathbb{S}^{2d}$. Balanced van Kampen-obstruction…