论文标题
凸的共同辅助表示3个群体组的表示
Convex co-compact representations of 3-manifold groups
论文作者
论文摘要
如果它具有有限的内核，并且其图像ACTS在真实的投影空间中正确凸面域上共同处理，则将有限生成的组的表示为凸出的通用线性群中，称为凸共划分。我们证明，只有在歧管是几何形状（带有欧几里得，双曲线或欧几里得$ \ times $ hyprobolic几何形状）或几何分解中的每个组件时，只有在歧管是几何形状（带有欧几里得，双曲线$ \ times $ \ times $ \ times $ \ times $ \ times $ \ time）的基本组中，几何学的基本组才能承认这种表示形式。在每种情况下，我们描述了此类示例的结构。
A representation of a finitely generated group into the projective general linear group is called convex co-compact if it has finite kernel and its image acts convex co-compactly on a properly convex domain in real projective space. We prove that the fundamental group of a closed irreducible orientable 3-manifold can admit such a representation only when the manifold is geometric (with Euclidean, Hyperbolic, or Euclidean $\times$ Hyperbolic geometry) or when every component in the geometric decomposition is hyperbolic. In each case, we describe the structure of such examples.
