论文标题
双曲线组和非紧凑型实际代数曲线
Hyperbolic Groups and Non-Compact Real Algebraic Curves
论文作者
论文摘要
在本文中，我们研究了非紧密的真实代数曲线的空间，即对$（p，τ）$，其中$ p $是带有有限数量的孔和穿刺的紧凑型riemann表面，$τ：p \ to p $是抗霍洛摩尔肌的屈服。我们描述了Fuchsian群体对非紧密的实际代数曲线的均匀化。我们构建非紧密的真实代数曲线的空间，并描述其连接的组件。我们证明，任何连接的组件都是通过离散组的有限维真实矢量空间的商同构的，并确定这些向量空间的尺寸。
In this paper we study the spaces of non-compact real algebraic curves, i.e. pairs $(P,τ)$, where $P$ is a compact Riemann surface with a finite number of holes and punctures and $τ:P\to P$ is an anti-holomorphic involution. We describe the uniformisation of non-compact real algebraic curves by Fuchsian groups. We construct the spaces of non-compact real algebraic curves and describe their connected components. We prove that any connected component is homeomorphic to a quotient of a finite-dimensional real vector space by a discrete group and determine the dimensions of these vector spaces.
