3 problems

Let $\phi$ be a pA mutation loop on a marked surface $\Sigma$. Write $\mathcal{E}_\phi^a$ for its associated asymptotic entropy and $\lambda_{\pi(\phi)}$ for the spectral radius of…

Let $w\text{?}$ be a point of $b2X_{(t_0)}(b2R^{\mathrm{trop}})$, and let $b3$ be a path representing a mutation loop. For the sign sequence $b5_{b3}(w)$, consider the matrices…

Let $b3_i:t_i\to t'_i$ $(i=1,2)$ be edge paths in the exchange graph $b4_I$ representing the same mutation loop $d\rm[b3_1]_{b2}=d\rm[b3_2]_{b2}$. A path is sign-stable when it has…