论文标题
注射空间的摩尔斯子集强烈签约
Morse subsets of injective spaces are strongly contracting
论文作者
论文摘要
我们表明，在且仅当它强烈收缩时，在注射度度量空间中的准晶格才是摩尔斯。由于映射班级组，更普遍地，层次双曲线群正确且均匀地绘制了赋形度度量空间，因此我们推断出相关的各种后果，例如，伪anosovs/morse元素的生长紧密度和一般性。此外，我们表明，注射式度量空间具有莫尔斯局部到全球特性，并且在注射度度空间上适当起作用的非虚拟环节群体是偶然的，只有它包含莫尔斯射线。
We show that a quasi-geodesic in an injective metric space is Morse if and only if it is strongly contracting. Since mapping class groups and, more generally, hierarchically hyperbolic groups act properly and coboundedly on injective metric spaces, we deduce various consequences relating, for example, to growth tightness and genericity of pseudo-Anosovs/Morse elements. Moreover, we show that injective metric spaces have the Morse local-to-global property and that a non-virtually-cyclic group acting properly and coboundedly on an injective metric space is acylindrically hyperbolic if and only it contains a Morse ray.
