论文标题
凸实际投影几何形状中相对双曲基团的结构
The structure of relatively hyperbolic groups in convex real projective geometry
论文作者
论文摘要
在本文中，我们证明了相对双曲基团（具有任意外围的亚组）在实际投射空间中正确凸面域上表现出幼稚凸的一般结构定理。我们还根据存在具有良好隔离属性的封闭无界凸子集的不变集合的存在来建立此类组的表征。这是$ {\ rm cat}（0）$ spaces的Hindawi-Hruska-kleiner结果的真正投影类似物。我们还获得了该组的Bowditch边界和理想边界商之间的同态同态。
In this paper we prove a general structure theorem for relatively hyperbolic groups (with arbitrary peripheral subgroups) acting naive convex co-compactly on properly convex domains in real projective space. We also establish a characterization of such groups in terms of the existence of an invariant collection of closed unbounded convex subsets with good isolation properties. This is a real projective analogue of results of Hindawi-Hruska-Kleiner for ${\rm CAT}(0)$ spaces. We also obtain an equivariant homeomorphism between the Bowditch boundary of the group and a quotient of the ideal boundary.
