11 problems

Nonnegativity conjecture for discrete pseudomanifolds.

Let $M$ be a $d$-dimensional complementary weak pseudomanifold, and let $\chi(M)$ denote its Euler characteristic. Euler characteristic conjecture. The Euler characteristic of $M$…

Let $X^n$ be a pseudomanifold and let $Y\subset X$ be a compact codimension-$1$ submanifold such that … where $Y\subset\subset X^{\mathrm{reg}}$. For a perversity function…

A complementary weak pseudomanifold is a weak pseudomanifold whose simplicial complex satisfies complementarity. Let $M$ be a $d$-dimensional complementary weak pseudomanifold with…

Let $P$ be a closed aspherical $n$-pseudomanifold with isolated singularities, and let $\widetilde P$ be its universal cover. Davis–Okun's conjecture. The $L^2$-homology of…

Let $M$ be a discrete $d$-manifold, with chromatic number denoted by $X(M)$. Let $\theta=\frac{3(d+1)}{2}$, and write $\lceil - \rceil$ for the ceiling function. Knill's tighter ch…

Let $k$ be a field of arbitrary characteristic, and let $\Delta$ be a connected oriented simplicial pseudomanifold over $k$ of dimension $d-1$ with vertex set $V$. For…

Let $\mathcal{P}^4_k$, $\mathcal{P}^3_k$, $\mathcal{P}^2_k$, and $\mathcal{P}^{3\,\mathrm{(NL)}}_k$ denote the four constructed series of triangulations discussed in the paper. In…

Let $\mathbbm{k}$ be any field of characteristic $p$, let $\varSigma$ be a $(d-1)$-dimensional pseudomanifold over $\mathbbm{k}$, and let $\mathbbm{k}[\varSigma]$ be its associated…

Let $\mathbbm{k}$ be any field, let $\varSigma$ be a $(d-1)$-dimensional pseudomanifold over $\mathbbm{k}$, and let $\mathbbm{k}[\varSigma]$ be its associated graded commutative fa…

Let $l\colon\bigsqcup_\alpha S_\alpha^1\hookrightarrow S^3$ be an arbitrary link, and let $K$ be the pseudo-manifold obtained by collapsing each component of the link to a point. L…