5 papers
A characterization of pseudo-Anosov mapping classes via tropical cluster transformations
Tsukasa Ishibashi, Shunsuke Kano
We give a characterization of generic pseudo-Anosov mapping classes purely in terms of their expressions in the shear coordinates, thus giving an answer to a problem raised by Papa…
Earthquake theorem for cluster algebras of finite type
Takeru Asaka, Tsukasa Ishibashi, Shunsuke Kano
We introduce a cluster algebraic generalization of Thurston's earthquake map for the cluster algebras of finite type, which we call the \emph{cluster earthquake map}. It is defined…
Skein and cluster algebras with coefficients for unpunctured surfaces
Tsukasa Ishibashi, Shunsuke Kano, Wataru Yuasa
We propose a skein model for the quantum cluster algebras of surface type with coefficients. We introduce a skein algebra of a walled surface $(Σ…
Unbounded -laminations around punctures
Tsukasa Ishibashi, Shunsuke Kano
We continue to study the unbounded -laminations [IK22], with a focus on their structures at punctures. A key ingredient is their relation to the root data of $\mat…
Unbounded -laminations and their shear coordinates
Tsukasa Ishibashi, Shunsuke Kano
Generalizing the work of Fock--Goncharov on rational unbounded laminations, we give a geometric model of the tropical points of the cluster variety $\mathcal{X}_{\mathfrak{sl}_3,Σ…