3 citations · 12 across the 10 of their papers we have counts for
10 papers
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…
Entropy of cluster DT transformations and the finite-tame-wild trichotomy of acyclic quivers
Tsukasa Ishibashi, Shunsuke Kano
The cluster algebra associated with an acyclic quiver has a special mutation loop , called the cluster Donaldson--Thomas (DT) transformation, related to the Auslander--Reiten tr…
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}…
Categorical dynamical systems arising from sign-stable mutation loops
Shunsuke Kano
We give an autoequivalence of the derived category of the Ginzburg dg algebra for a mutation loop satisfying the sign stability introduced in [IK21]. We compute the categorical ent…
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…
Algebraic entropy of sign-stable mutation loops
Tsukasa Ishibashi, Shunsuke Kano
We introduce a property of mutation loops, called the sign stability, with a focus on an asymptotic behavior of the iteration of the tropical -transformation. A sign-s…