7 problems

Let $n_1\geq n_2>2$, and consider the $T_{n_1,n_2,2}$ quivers associated with the indicated Legendrian links. Let $\Gamma_\tau$ be the subgroup generated by the tail automorphisms.…

Let $\mathbb{A}$ be a cluster algebra admitting a $T_{\mathbf n}$ quiver, let $\Gamma_\tau$ be the abelian subgroup generated by the tail automorphisms $\tau_1,\ldots,\tau_k$, and…

Let $K$subset a contact manifold be a knot or link, let $\operatorname{Leg}(K)$ be the space of Legendrian embeddings of $K$, and let $\Lambda(\beta)$ be a maximal-Thurston--Benneq…

Let $T_{\boldsymbol{n},\boldsymbol{w}}$ be a quiver of the indicated type, let $\chi(T_{\boldsymbol{n},\boldsymbol{w}})$ be its associated quantity, and let…

Let $T_{\boldsymbol{n},\boldsymbol{w}}$ be a quiver associated with equal-length vectors of positive integers, and let…

Let $\boldsymbol{n}$ and $\boldsymbol{w}$ be equal-length vectors of positive integers, and let $T_{\boldsymbol{n},\boldsymbol{w}}$ be the associated quiver. Write … Let…

Let ${\widehat\Gamma}_{X_6}$ be the saturated cluster modular group of type $X_6$, and let $\Gamma_{X_6}$ be the cluster modular group of type $X_6$. A cluster Dehn twist is an inf…