Symplectic structure on the character varieties of Sasakian threefolds
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913073291329536 |
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| author | Biswas, Indranil Sengupta, Ambar N. |
| author_facet | Biswas, Indranil Sengupta, Ambar N. |
| contents | Take a compact Sasakian threefold $M$ and consider the associated irreducible $\text{SL}(r,{\mathbb C})$-character variety ${\mathcal R} := \text{Hom}(π_1(M, x_0), \text{SL}(r, {\mathbb C}))^{ir}/ \text{SL}(r, {\mathbb C})$ of $M$, where $\text{Hom}(π_1(M, x_0), \text{SL}(r, {\mathbb C}))^{ir}$ is the space of irreducible homomorphisms. We first construct a natural algebraic $2$-form on $\mathcal R$. Then it is shown that this $2$--form is closed. Finally we show that the restriction of this $2$--form to $\text{Hom}(π_1(M, x_0), \text{SU}(r))^{ir}$ is symplectic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_27081 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Symplectic structure on the character varieties of Sasakian threefolds Biswas, Indranil Sengupta, Ambar N. Differential Geometry Symplectic Geometry Take a compact Sasakian threefold $M$ and consider the associated irreducible $\text{SL}(r,{\mathbb C})$-character variety ${\mathcal R} := \text{Hom}(π_1(M, x_0), \text{SL}(r, {\mathbb C}))^{ir}/ \text{SL}(r, {\mathbb C})$ of $M$, where $\text{Hom}(π_1(M, x_0), \text{SL}(r, {\mathbb C}))^{ir}$ is the space of irreducible homomorphisms. We first construct a natural algebraic $2$-form on $\mathcal R$. Then it is shown that this $2$--form is closed. Finally we show that the restriction of this $2$--form to $\text{Hom}(π_1(M, x_0), \text{SU}(r))^{ir}$ is symplectic. |
| title | Symplectic structure on the character varieties of Sasakian threefolds |
| topic | Differential Geometry Symplectic Geometry |
| url | https://arxiv.org/abs/2604.27081 |