4 problems

Global cone conjecture for moduli spaces of simple polygons. ${\mathcal M}(n)$ is homeomorphic to $C(\mathbb{S}^{2n-5}/\langle\Sigma,T\rangle)$. A local version holds in a neighbor…

Let $S(n)$ be the connected component of the space of simple labeled $n$-gons modulo oriented similarity consisting of positively oriented polygons. As an open subset of…

Let $X_{a,b}(\ell)$ be a big polygon space associated with a length vector $\ell$, let $T$ be the acting torus, and let $\mu(\ell)$ denote the invariant introduced in the paper. Th…

Nonexistence conjecture. For an arbitrary $n$ with $n\geq n_0$, where $n_0$ is sufficiently large, the isotopy of Theorem 1 is not valid, even without the additional requirements t…