On a Remarkable Polyhedron Geometrizing the Figure Eight Knot Cone Manifolds
On a Remarkable Polyhedron Geometrizing the Figure Eight Knot Cone Manifolds
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关于八字形节锥流形几何化的非凡多面体
DOI：
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发表时间：
1995
影响因子：
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通讯作者：
T. Lozano
中科院分区：
文献类型：
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作者：
T. Lozano
我们定义了一个单参数的多面体族P（t），它们存在于三维常曲率空间C（t）中。通过等距在P（t）中成对地识别面产生锥流形M（t）（锥流形很像orbifold）。拓扑上M（t）是S3，它有一个奇异集，即8字形纽结.当t变化时，曲率取每一个真实的值。在t = −1时，我们称之为自发手术的现象发生了，M（t）的拓扑类型发生了变化。我们讨论了这一点的影响。
We define a one parameter family of polyhedra P (t) that live in three dimensional spaces of constant curvature C(t). Iden- tifying faces in pairs in P (t) via isometries gives rise to a cone manifold M(t) (A cone manifold is much like an orbifold.). Topologically M(t) is S 3 and it has a singular set that is the figure eight knot. As t varies, curvature takes on every real value. At t = −1 a phenomenon which we call spontaneous surgery occurs and the topological type of M(t) changes. We discuss the implications of this.