Bounded $\mathfrak{sp}_4$-laminations and their intersection coordinates
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909814833020928 |
|---|---|
| author | Ishibashi, Tsukasa Sun, Zhe Yuasa, Wataru |
| author_facet | Ishibashi, Tsukasa Sun, Zhe Yuasa, Wataru |
| contents | We introduce rational bounded $\mathfrak{sp}_4$-laminations on a marked surface $\boldsymbolΣ$ as a proposed topological model for the rational tropical points $\mathcal{A}_{Sp_4,\boldsymbolΣ}(\mathbb{Q}^{\mathsf{T}})$ of the Fock--Goncharov moduli space [FG06]. Our space consists of certain equivalence classes of $\mathfrak{sp}_4$-webs introduced by Kuperberg [Kup96], together with rational measures. We define tropical coordinate systems using the $\mathfrak{sp}_4$-case of the intersection number of Shen--Sun--Weng [SSW25], and establish a bijection using the framework of the graded $\mathfrak{sp}_4$-skein algebra. This provides a topological perspective for Fock--Goncharov duality for $\mathfrak{sp}_4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_25014 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bounded $\mathfrak{sp}_4$-laminations and their intersection coordinates Ishibashi, Tsukasa Sun, Zhe Yuasa, Wataru Algebraic Geometry Geometric Topology Quantum Algebra Representation Theory We introduce rational bounded $\mathfrak{sp}_4$-laminations on a marked surface $\boldsymbolΣ$ as a proposed topological model for the rational tropical points $\mathcal{A}_{Sp_4,\boldsymbolΣ}(\mathbb{Q}^{\mathsf{T}})$ of the Fock--Goncharov moduli space [FG06]. Our space consists of certain equivalence classes of $\mathfrak{sp}_4$-webs introduced by Kuperberg [Kup96], together with rational measures. We define tropical coordinate systems using the $\mathfrak{sp}_4$-case of the intersection number of Shen--Sun--Weng [SSW25], and establish a bijection using the framework of the graded $\mathfrak{sp}_4$-skein algebra. This provides a topological perspective for Fock--Goncharov duality for $\mathfrak{sp}_4$. |
| title | Bounded $\mathfrak{sp}_4$-laminations and their intersection coordinates |
| topic | Algebraic Geometry Geometric Topology Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/2509.25014 |