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Invariants of\/ {\large${\rm PSL}_n\mathbb{R}$}-Fuchsian Representations\\ and a Slice of Hitchin Components
http://hdl.handle.net/2261/0002005799
http://hdl.handle.net/2261/000200579910e97eb6-3bf9-4d88-b9d3-9b2a80f88d89
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jms280403.pdf (338.9 KB)
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Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||||
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公開日 | 2022-10-25 | |||||||
タイトル | ||||||||
タイトル | Invariants of\/ {\large${\rm PSL}_n\mathbb{R}$}-Fuchsian Representations\\ and a Slice of Hitchin Components | |||||||
言語 | en | |||||||
言語 | ||||||||
言語 | eng | |||||||
キーワード | ||||||||
言語 | en | |||||||
主題Scheme | Other | |||||||
主題 | Hitchin components | |||||||
キーワード | ||||||||
言語 | en | |||||||
主題Scheme | Other | |||||||
主題 | Teichm\"uller spaces | |||||||
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資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||||
資源タイプ | departmental bulletin paper | |||||||
著者 |
Inagaki, Yusuke
× Inagaki, Yusuke
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著者所属 | ||||||||
言語 | en | |||||||
値 | Graduate School of Science, Osaka University | |||||||
抄録 | ||||||||
内容記述タイプ | Abstract | |||||||
内容記述 | The Hitchin component $H_n(S)$ is a special component of the ${\rm PSL}_n\mathbb{R}$-character variety of a closed surface $S$ of genus $g \geq 2$ which contains the discrete faithful representations $\pi_1(S) \rightarrow {\rm PSL}_2\mathbb{R}$ via an irreducible representation. Bonahon-Dreyer (\cite{BD14}, \cite{BD17}) gave a parameterization of $H_n(S)$ by the triangle invariants and the shearing-type invariants fixing an arbitrary maximal geodesic lamination on $S$, so that the Hitchin component is a cone in a Euclidean space. The images of discrete faithful representations $\pi_1(S) \rightarrow {\rm PSL}_2\mathbb{R}$ in $H_n(S)$ are called $\PSL_n\R$-Fuchsian representations. In this paper we characterize the $\PSL_n\R$-Fuchsian representations of the Hitchin component in the Bonahon-Dreyer coordinates. In particular this explicit characterization implies the set of the $\PSL_n\R$-Fuchsian representations is an affine slice. We also discuss the case when $S$ has boundary. |
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言語 | en | |||||||
書誌情報 |
en : Journal of Mathematical Sciences The University of Tokyo 巻 28, 号 4, p. 593-639, 発行日 2021-10-05 |
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収録物識別子タイプ | ISSN | |||||||
収録物識別子 | 13405705 | |||||||
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収録物識別子タイプ | NCID | |||||||
収録物識別子 | AA11021653 | |||||||
Mathmatical Subject Classification | ||||||||
言語 | en | |||||||
値 | 57N16(MSC2010) | |||||||
Mathmatical Subject Classification | ||||||||
言語 | en | |||||||
値 | 22E40(MSC2010) | |||||||
出版者 | ||||||||
出版者 | Graduate School of Mathematical Sciences, The University of Tokyo | |||||||
言語 | en | |||||||
原稿受領日 | ||||||||
値 | 2020-07-28 |