6 problems

Let $C$ be a $c$-chain in $\mathbb{R}^d$ with $c<d$, and let $U$ be a finite set of points in $\mathbb{R}^d$ in strong general position with respect to $C$. Simplicial-chain realiz…

Let $c,n,d$ be non-negative integers such that $c<d$. Let $C$ be a $c$-chain in $d53d^d$, let $N$ be an $n$-dimensional closed PL manifold, and let $f:N\tod53d^d-\partial C$ be a P…

Generic total H-complexity conjecture. With probability $1$, the total $H$-complexity of $F$ is less than or equal to the number of $0$-cells of $\mathcal{C}(F)$.

Coarse bounded H-complexity conjecture. The coarse bounded sublevel $H$-complexity (respectively, the coarse bounded superlevel $H$-complexity) of $F$ is a lower bound for the glob…

Lutz–Nevo conjecture. The following are equivalent:

Let $(K3)_{16}$ and $(K3)_{17}$ denote the simplicial complexes with $16$ and $17$ vertices, respectively, constructed in the dilatation process described in the paper. The PL-equi…