2020年11月5日
Density of g-Vector Cones From Triangulated Surfaces
International Mathematics Research Notices
- 巻
- 2020
- 号
- 21
- 開始ページ
- 8081
- 終了ページ
- 8119
- 記述言語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1093/imrn/rnaa008
- 出版者・発行元
- Oxford University Press (OUP)
<title>Abstract</title>
We study $g$-vector cones associated with clusters of cluster algebras defined from a marked surface $(S,M)$ of rank $n$. We determine the closure of the union of $g$-vector cones associated with all clusters. It is equal to $\mathbb{R}^n$ except for a closed surface with exactly one puncture, in which case it is equal to the half space of a certain explicit hyperplane in $\mathbb{R}^n$. Our main ingredients are laminations on $(S,M)$, their shear coordinates, and their asymptotic behavior under Dehn twists. As an application, if $(S,M)$ is not a closed surface with exactly one puncture, the exchange graph of cluster tilting objects in the corresponding cluster category is connected. If $(S,M)$ is a closed surface with exactly one puncture, it has precisely two connected components.
We study $g$-vector cones associated with clusters of cluster algebras defined from a marked surface $(S,M)$ of rank $n$. We determine the closure of the union of $g$-vector cones associated with all clusters. It is equal to $\mathbb{R}^n$ except for a closed surface with exactly one puncture, in which case it is equal to the half space of a certain explicit hyperplane in $\mathbb{R}^n$. Our main ingredients are laminations on $(S,M)$, their shear coordinates, and their asymptotic behavior under Dehn twists. As an application, if $(S,M)$ is not a closed surface with exactly one puncture, the exchange graph of cluster tilting objects in the corresponding cluster category is connected. If $(S,M)$ is a closed surface with exactly one puncture, it has precisely two connected components.
- リンク情報
-
- DOI
- https://doi.org/10.1093/imrn/rnaa008
- URL
- http://academic.oup.com/imrn/article-pdf/2020/21/8081/34303338/rnaa008.pdf
- Scopus
- https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85095278994&origin=inward
- Scopus Citedby
- https://www.scopus.com/inward/citedby.uri?partnerID=HzOxMe3b&scp=85095278994&origin=inward
- ID情報
-
- DOI : 10.1093/imrn/rnaa008
- ISSN : 1073-7928
- eISSN : 1687-0247
- SCOPUS ID : 85095278994