The Hitchin component $$\mathrm {Hit}_n(S)$$ Hit n ( S ) of a closed surface S is a preferred component of the character variety $$\mathcal {X}_{\mathrm {PSL}_n(\mathbb {R})}(S)$$ X PSL n ( R ) ( S ) consisting of homomorphisms from the fundamental group $$\pi _1(S)$$ π 1 ( S ) to the Lie group $$\mathrm {PSL}_n(\mathbb {R})$$ PSL n ( R ) , whose elements enjoy remarkable geometric and dynamical properties. We consider a certain type of deformations of the elements of $$\mathrm {Hit}_n(S)$$ Hit n ( S ) , called shearing deformations, and compute their pairing for the Atiyah–Bott–Goldman symplectic form of the character variety.

中文翻译：

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Hitchin 表示的剪切变形和 Atiyah-Bott-Goldman 辛形式

闭合曲面 S 的 Hitchin 分量 $$\mathrm {Hit}_n(S)$$ Hit n ( S ) 是字符变体 $$\mathcal {X}_{\mathrm {PSL}_n( \mathbb {R})}(S)$$ X PSL n ( R ) ( S ) 由从基本群 $$\pi _1(S)$$ π 1 ( S ) 到李群 $$\ 的同态组成mathrm {PSL}_n(\mathbb {R})$$ PSL n ( R ) ，其元素具有非凡的几何和动力学特性。我们考虑 $$\mathrm {Hit}_n(S)$$ Hit n ( S ) 的元素的某种类型的变形，称为剪切变形，并计算它们对字符的 Atiyah-Bott-Goldman 辛形式的配对种类。