AI 中文总结
该研究关联闭3-流形动力学与同调内臓，构造典范半流并证明其在Thurston开锥上的不变性，应用其结构编码伪Anosov流的特定闭轨道，还确定了正类对应的半流增长率。
AI 中文摘要
我们将闭3-流形上的动力学与Agol和Zhang提出的拓扑不变量——同调内臓（homology guts）关联起来。给定一个容许无完美拟合的伪Anosov流φ的闭流形M，我们构造了与φ所承载的同调类相关联的、定义在同调内臓上的典范半流。我们证明，除半环外的轨道等价类下，内臓上的半流在每个Thurston开锥上是不变的。作为应用，同调内臓的基本群与缝合结构编码了φ的特定类型闭轨道。此外，对于H¹(M)中的正类，内臓上的典范半流具有明确定义的增长率。
英文摘要
We relate the dynamics on a closed 3-manifold to the topological invariant, homology guts, proposed by Agol and Zhang. Given a closed manifold $M$ that admits a pseudo-Anosov flow $φ$ without perfect fits, we construct a canonical semiflow on the homology guts associated to homology classes carried by $φ$. We show that, up to orbit equivalent outside half annuli, the semiflow on the guts is invariant on each Thurston open cone. As an application, the fundamental group and the sutured structure of homology guts encode closed orbits of $φ$ with particular type. Besides, for a positive class in $H^{1}(M)$, the canonical semiflow on the guts has a well-defined growth rate.
Comments50 pages, 20 figures. Comments are welcome!
