4 problems

Let $P$ be a flexible polyhedron in one of the constant-curvature spaces $\mathbb{E}^n$, $\mathbb{S}^n$, or $\mathbbl{\Lambda}^n$. Two polyhedra are scissors congruent if they can…

Let $P_*(S^d)$ denote Goncharov's Dehn complex, and let $P_*(S^{2n-1})$ be its spherical version. Write $gr^gamma_n K_{n+m}(C)_Q$ for the $n$-th graded piece of the $gamma$-filtrat…

Weak Strong Bellows Conjecture. The Dehn invariant of any flexible polyhedron remains constant during the flexion. This is a weaker form of the Strong Bellows Conjecture, since sci…

Let $M_n$ and $M_I$, for $I\in\{0,1,2\}^{n+1}$, be the hyperbolic manifolds described in the paper. Since they decompose along totally geodesic surfaces into isometric pieces, they…