On Character Variety of Anosov Representations
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916668961193984 |
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| author | Gongopadhyay, Krishnendu Nayak, Tathagata |
| author_facet | Gongopadhyay, Krishnendu Nayak, Tathagata |
| contents | Let $Γ$ be the fundamental group of a $k$-punctured, $k \geq 0$, closed connected orientable surface of genus $g \geq 2$. We show that the character variety of the $(Q^+, Q^-)$-Anosov irreducible representations, resp. the character variety of the $(P^+, P^-)$-Anosov Zariski dense representations of $Γ$ into $\SL(n , \C)$, $n \geq 2$, is a complex manifold of complex dimension \hbox{$(2g+k-2)(n^2-1)$}. For $Γ=π_1(Σ_g)$, we also show that these character varieties are holomorphic symplectic manifolds. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_07316 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Character Variety of Anosov Representations Gongopadhyay, Krishnendu Nayak, Tathagata Geometric Topology Complex Variables Differential Geometry Group Theory Representation Theory 22F30 (Primary) 22E46, 32G15, 20C15 (Secondary) Let $Γ$ be the fundamental group of a $k$-punctured, $k \geq 0$, closed connected orientable surface of genus $g \geq 2$. We show that the character variety of the $(Q^+, Q^-)$-Anosov irreducible representations, resp. the character variety of the $(P^+, P^-)$-Anosov Zariski dense representations of $Γ$ into $\SL(n , \C)$, $n \geq 2$, is a complex manifold of complex dimension \hbox{$(2g+k-2)(n^2-1)$}. For $Γ=π_1(Σ_g)$, we also show that these character varieties are holomorphic symplectic manifolds. |
| title | On Character Variety of Anosov Representations |
| topic | Geometric Topology Complex Variables Differential Geometry Group Theory Representation Theory 22F30 (Primary) 22E46, 32G15, 20C15 (Secondary) |
| url | https://arxiv.org/abs/2409.07316 |