We study the monodromy of the Hitchin fibration for moduli spaces of parabolic G-Higgs bundles in the cases when $G=\text{SL}(2,\mathbb{R})$, $\text{GL}(2,\mathbb{R})$ and $\text{PGL}(2,\mathbb{R})$. A calculation of the orbits of the monodromy with ${\mathbb{Z}}_2$-coefficients provides an exact count of the components of the moduli spaces for these groups.

中文翻译：

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2 阶抛物线 Hitchin 系统的单向性

我们研究了抛物线G- Higgs 丛的模空间的 Hitchin 纤维化的单向性，当$G=\text{SL}(2,\mathbb{电阻})$, $\text{GL}(2,\mathbb{电阻})$ 和 $\text{PGL}(2,\mathbb{电阻})$. 单向性轨道的计算${\mathbb{Z}}_2$-coefficients 提供这些组的模空间分量的精确计数。