论文标题
弯曲Teichmüller空间和角色品种
Bending Teichmüller spaces and character varieties
论文作者
论文摘要
We consider the mapping $b_L\colon\mathcal{T} \to χ$ of the Fricke-Teichmüller space $\mathcal{T}$ into the $\mathrm{PSL}_2\mathbb{C}$-character variety $χ$ of the surface, obtained by holonomy representations of bent hyperbolic surfaces along a fixed measured lamination $ L $。我们证明，该映射是一个均衡的真实实验室分析嵌入，并且对于几乎所有测量的层压板，适当。 此外，我们还表明，此“是映射” $ b_l \ colon \ Mathcal {t} \χ$连续扩展到从$ \ Mathcal {t} $的thurston边界的映射到几乎无处不在的身份图。 此外，我们将真实的分析子变量$ {\ rm im} \，b_l $在symplecitcaly嵌入到产品中，通过复杂共轭扭曲的对角线映射将其嵌入产品$χ\ timesχ$。更确切地说，我们几何地构建了一个封闭的$ \ mathbb {C} $ - 符合$ {\ rm im} \，b_l $的$χ\ timesχ$的sympletic复杂分析子变量作为半维真实分析的b_l $。
We consider the mapping $b_L\colon\mathcal{T} \to χ$ of the Fricke-Teichmüller space $\mathcal{T}$ into the $\mathrm{PSL}_2\mathbb{C}$-character variety $χ$ of the surface, obtained by holonomy representations of bent hyperbolic surfaces along a fixed measured lamination $L$. We prove that this mapping is an equivariant symplectic real-analytic embedding, and, for almost all measured laminations, proper. In addition, we show that this "being map'' $b_L\colon \mathcal{T} \to χ$ continuously extends to a mapping from Thurston's boundary of $\mathcal{T}$ to the Morgan-Shalen boundary of $χ$ as the identity map almost everywhere. Moreover, we complexify the real analytic subvariety ${\rm Im}\, b_L$ after symplecitcaly embedding it in the product variety $χ\times χ$ by the diagonal mapping twisted by complex conjugation. More precisely, we geometrically construct a closed $\mathbb{C}$-symplectic complex analytic subvariety of $χ\times χ$ containing ${\rm Im}\, b_L$ as a half-dimensional real analytic subvariety.
