3 citations · 12 across the 10 of their papers we have counts for
6 papers · 1 filter
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,\…
Train track combinatorics and cluster algebras
Shunsuke Kano
The concepts of train track was introduced by W. P. Thurston to study the measured foliations/laminations and the pseudo-Anosov mapping classes on a surface. In this paper, we tran…
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…
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}…
Sign stability of mapping classes on marked surfaces II: general case via reductions
Tsukasa Ishibashi, Shunsuke Kano
We give a cluster algebraic description of the reduction procedure of mapping classes along a multicurve. Based on this description, we characterize pseudo-Anosov mapping classes o…
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…