On the domination of surface-group representations in $\mathrm{PU}(2,1)$
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908598301360128 |
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| author | Barman, Pabitra Gongopadhyay, Krishnendu |
| author_facet | Barman, Pabitra Gongopadhyay, Krishnendu |
| contents | This article explores surface-group representations into the complex hyperbolic group $\mathrm{PU}(2,1)$ and presents domination results for a special class of representations called $T$-bent representations. Let $S_{g,k}$ be a punctured surface of negative Euler characteristic. We prove that for a $T$-bent representation $ρ: π_1(S_{g,k}) \rightarrow \mathrm{PU}(2,1)$, there exists a discrete and faithful representation $ρ_0: π_1(S_{g,k}) \rightarrow \mathrm{PO}(2,1)$ that dominates $ρ$ in the Bergman translation length spectrum, while preserving the lengths of the peripheral loops. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_03838 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the domination of surface-group representations in $\mathrm{PU}(2,1)$ Barman, Pabitra Gongopadhyay, Krishnendu Geometric Topology Primary 20H10, Secondary 51M10, 30F40 This article explores surface-group representations into the complex hyperbolic group $\mathrm{PU}(2,1)$ and presents domination results for a special class of representations called $T$-bent representations. Let $S_{g,k}$ be a punctured surface of negative Euler characteristic. We prove that for a $T$-bent representation $ρ: π_1(S_{g,k}) \rightarrow \mathrm{PU}(2,1)$, there exists a discrete and faithful representation $ρ_0: π_1(S_{g,k}) \rightarrow \mathrm{PO}(2,1)$ that dominates $ρ$ in the Bergman translation length spectrum, while preserving the lengths of the peripheral loops. |
| title | On the domination of surface-group representations in $\mathrm{PU}(2,1)$ |
| topic | Geometric Topology Primary 20H10, Secondary 51M10, 30F40 |
| url | https://arxiv.org/abs/2506.03838 |