论文标题
低维磁铁歧管
Low-dimensional solenoidal manifolds
论文作者
论文摘要
在本文中，我们调查了$ n $二维的电磁歧管，价格为$ n = 1,2 $和3，并介绍了有关它们的新结果。尺寸$ n $的电磁歧管是以坎托套件和开放$ n $维磁盘的产品为模型的当地建模的公制空间。因此，它们可以通过$ n $维的叶子“层压”（或“叶”）。通过A. clark和S. hurder的定理，拓扑均匀的紧凑型电磁歧管是麦考德电磁阀，即作为有限层的较小塔的倒数层的倒数，该塔是有限的，正常的紧凑型歧管，具有无限和残留有限的和残留有限的和残留有限的基本组。在这种情况下，它们的结构非常丰富，因为它们是紧凑型歧管上的主要康托尔组捆绑包，并且它们的行为就像“层压”版本的紧凑型歧管，因此它们具有许多特性。这些对象将歧管的可辨别性属性编码。
In this paper we survey $n$-dimensional solenoidal manifolds for $n=1,2$ and 3, and present new results about them. Solenoidal manifolds of dimension $n$ are metric spaces locally modeled on the product of a Cantor set and an open $n$-dimensional disk. Therefore, they can be "laminated" (or "foliated") by $n$-dimensional leaves. By a theorem of A. Clark and S. Hurder, topologically homogeneous, compact solenoidal manifolds are McCord solenoids i.e. are obtained as the inverse limit of an increasing tower of finite, regular covers of a compact manifold with an infinite and residually finite fundamental group. In this case their structure is very rich since they are principal Cantor-group bundles over a compact manifold and they behave like "laminated" versions of compact manifolds, thus they share many of their properties. These objects codify the commensurability properties of manifolds.
