12 citations · 44 across the 21 of their papers we have counts for
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Fixed point theorem for cluster modular groups
Tsukasa Ishibashi
We prove that any finite subgroup of the cluster modular group has fixed points in the cluster manifolds $\mathcal{A}_{\boldsymbol{s}}(\mathbb{R}_{>0…
Adjoint Reidemeister torsion of 3-manifolds with torus boundary for semisimple algebraic groups
Tsukasa Ishibashi, Yuma Mizuno
Let be a compact oriented -manifold with boundary consisting of tori, and let be a semisimple algebraic group. We define the adjoint torsion function on the moduli stack…
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,\…
Quantum duality maps, skein algebras and their ensemble compatibility
Tsukasa Ishibashi, Hiroaki Karuo
We generalize the quantum duality map of Allegretti--Kim [AK17] for punctured closed surfaces to general marked surfaces. When the marked surface has no…
Teichmüller and lamination spaces with pinnings
Tsukasa Ishibashi
We describe the spaces of the positive and tropical points of the moduli space introduced by Goncharov--Shen [GS19] as certain Teichmüller and lamination sp…
Skein and cluster algebras of unpunctured surfaces for
Tsukasa Ishibashi, Wataru Yuasa
Continuing to our previous work [IY21](arXiv:2101.00643) on the -case, we introduce a skein algebra consisting of $\mathfrak{…
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}…
Skein and cluster algebras of unpunctured surfaces for
Tsukasa Ishibashi, Wataru Yuasa
For an unpunctured marked surface , we consider a skein algebra consisting of -webs on with the boundary skein relat…
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…
On a Nielsen-Thurston classification theory for cluster modular groups
Tsukasa Ishibashi
We classify elements of a cluster modular group into three types. We characterize them in terms of fixed point property of the action on the tropical compactifications associated w…