论文标题
有界抛物线点的爆炸
Equivariant blowups of bounded parabolic points
论文作者
论文摘要
让$ g $为同构在Hausdorff紧凑型空间$ z $上表现的团体。我们构建了一个新的空间$ x $，该$ x $炸毁了$ z $的有限抛物线点。这意味着，这意味着，$ g $由同构在$ x $上表现出来，并且存在连续的epoivariant map $π：x \ rightarrow z $，以至于每个非限制的抛物线寄生虫点$ z \ in z $，$ \＃point $ z \ in $ \＃point $ \ \＃π^{ - 1}（-1}（z）= 1 $。我们使用这种构造来表征一些$ g $与融合属性一起作用的空间，并构建$ g $的新收敛动作。作为一个应用程序之一，如果$ g $是一个组，而$ p $是$ g $的端空间的有界抛物线点，那么$ p $的稳定器是一项端。
Let $G$ be a group acting by homeomorphisms on a Hausdorff compact space $Z$. We constructed a new space $X$ that blows up equivariantly the bounded parabolic points of $Z$. This means, roughly speaking, that $G$ acts by homeomorphisms on $X$ and there exists a continuous equivariant map $π: X \rightarrow Z$ such that for every non bounded parabolic point $z \in Z$, $\#π^{-1}(z) = 1$. We use such construction to characterize topologically some spaces that $G$ acts with the convergence property and to construct new convergence actions of $G$ from old ones. As one of the applications, if $G$ is a group and $p$ is a bounded parabolic point of the space of ends of $G$, then the stabilizer of $p$ is one-ended.
