论文标题
恩格尔歧管中的横向托里
Transverse tori in Engel manifolds
论文作者
论文摘要
我们表明，恩格尔4个manifolds中的托里与触点的结构相似：每个具有琐碎正常束的圆环都是同位素的同位素，对于无限的许多不同的横向托里，其正式的不变人数在本地区分（全球范围内）。 （以前很少知道横向托里的例子。）我们对形式不变式进行了分类，这些不变性比横向结富。我们表明，在一个固定的恩格尔结构中，直到通过此类结构达到同质性，这些不变性是一组完整的唯一性障碍，并且每个具有微不足道的正常束的圆环都可以横向实现这些不变的任何组合。固定恩格尔结构未知的结构，我们探索了给定托里的主要不变性范围。样本应用是，许多恩格尔流形允许无限的许多横向横向横向tori类别，使每个类都包含无限的许多横向同位素类别。
We show that tori in Engel 4-manifolds behave analogously to knots in contact 3-manifolds: Every torus with trivial normal bundle is isotopic to infinitely many distinct transverse tori, distinguished locally (and globally in the nullhomologous case) by their formal invariants. (Few examples of transverse tori were previously known.) We classify the formal invariants, which are richer than for transverse knots. We show that in an overtwisted Engel structure, up to homotopy through such structures, these invariants are a complete set of uniqueness obstructions, and every torus with trivial normal bundle can be made transverse realizing any combination of these invariants. Fixing Engel structures not known to be overtwisted, we explore the range of the primary invariants of given tori. A sample application is that many Engel manifolds admit infinitely many transverse homotopy classes of unknotted transverse tori such that each class contains infinitely many transverse isotopy classes.
