论文标题
在图八节补充空间和非传播的Anosov流向Franks-Williams歧管上的非传播的Anosov分类中分类扩展的吸引子
Classifying expanding attractors on figure eight knot complement space and non-transitive Anosov flows on Franks-Williams manifold
论文作者
论文摘要
图8结空间（$ n_0 $）的路径闭合支持自然的DA（源自Anosov）扩展的吸引子。弗兰克斯·威廉姆斯（Franks-Williams）使用这种吸引子，在歧管$ m_0 $上构建了第一个非传递性anosov流的例子，该示例是通过沿其边界的身份图粘合两个$ n_0 $的$ n_0 $获得的，由弗兰克斯·威廉姆斯（Franks-Williams）命名。在本文中，我们的主要目标是对$ n_0 $的扩展吸引子进行分类，并在$ m_0 $上流动非传递性Anosov。我们证明，直到轨道等效性，DA扩展的吸引子是由$ N_0 $支持的独特扩展吸引子，而Franks和Williams构建的非交易性Anosov流是$ M_0 $ $ M_0 $的独特非交易性Anosov流。此外，还讨论了更多的一般情况。特别是，我们将非传递性的Anosov完全分类为一个无限多种环形的$ 3 $ manifolds的家族，并带有两个双曲线作品，通过通过任何粘合的同构粘合$ n_0 $粘贴了两份$ n_0 $。
The path closure of figure eight knot complement space, $N_0$, supports a natural DA (derived from Anosov) expanding attractor. Using this attractor, Franks-Williams constructed the first example of non-transitive Anosov flow on the manifold $M_0$ obtained by gluing two copies of $N_0$ through identity map along their boundaries, named by Franks-Williams manifold. In this paper, our main goal is to classify expanding attractors on $N_0$ and non-transitive Anosov flows on $M_0$. We prove that, up to orbit-equivalence, the DA expanding attractor is the unique expanding attractor supported by $N_0$, and the non-transitive Anosov flow constructed by Franks and Williams is the unique non-transitive Anosov flow admitted by $M_0$. Moreover, more general cases are also discussed. In particular, we completely classify non-transitive Anosov flows on a family of infinitely many toroidal $3$-manifolds with two hyperbolic pieces, obtained by gluing two copies of $N_0$ through any gluing homeomorphism.
