4 problems

Let ${\mathcal L}$ be a lattice and let $C$ be a crosscut of ${\mathcal L}$. Write $\Gamma(C,{\mathcal L})$ for the crosscut complex, $\operatorname{Bd}(\Gamma(C,{\mathcal L}))$ fo…

Let $\{X_i\}_{i=1}^\infty$ be a family of finite simplicial complexes. The strong NE-equivalence conjecture. There exists an infinite family of finite simplicial complexes…

Let $X$ and $Y$ be finite simplicial complexes. The NE-equivalence conjecture. There exist finite simplicial complexes $X$ and $Y$ having the same simple homotopy type, such that…

Zeeman's conjecture. After taking finitely many barycentric subdivisions, the product