论文标题
在2-孔子上的凸影结构的变形空间上的符号坐标
Symplectic coordinates on the deformation spaces of convex projective structures on 2-orbifolds
论文作者
论文摘要
令$ \ mathcal {o} $为封闭的否定Euler特性的2个孔。 huebschmann在变形空间$ \ mathcal {c}（\ Mathcal {O}）$ \ \ Mathcal {o} $上的变形空间$ \ MATHCAL {C}（\ MATHCAL {O}）$上构建了Atiyah-Bott-Goldman类型symbletic form $ω$。我们表明，$ \ Mathcal {o}上的凸影射击结构的变形空间$ \ MATHCAL {C}（\ MATHCAL {O}）$在$ \ mathcal {o}上允许与$ω$相对于$ω$。为此，我们表明$ \ Mathcal {C}（\ Mathcal {O}）$可以分解为较小的符号空间。在证明过程中，我们还研究了一个olbifold $ \ Mathcal {o} $的变形空间$ \ MATHCAL {C}（\ MATHCAL {O}）$，并使用边界进行边界，并在$ \ Mathcal {o \ Mathcal {o {o \ Mathcal of consevex Projective of Condeive of Briender {o {o {o {o）上构建符号形式。
Let $\mathcal{O}$ be a closed orientable 2-orbifold of negative Euler characteristic. Huebschmann constructed the Atiyah-Bott-Goldman type symplectic form $ω$ on the deformation space $\mathcal{C}(\mathcal{O})$ of convex projective structures on $\mathcal{O}$. We show that the deformation space $\mathcal{C}(\mathcal{O})$ of convex projective structures on $\mathcal{O}$ admits a global Darboux coordinates system with respect to $ω$. To this end, we show that $\mathcal{C}(\mathcal{O})$ can be decomposed into smaller symplectic spaces. In the course of the proof, we also study the deformation space $\mathcal{C}(\mathcal{O})$ for an orbifold $\mathcal{O}$ with boundary and construct the symplectic form on the deformation space of convex projective structures on $\mathcal{O}$ with fixed boundary holonomy.
