THE THIRD POWER OF THE SMALE HORSESHOE INDUCES ALL LINK TYPES
THE THIRD POWER OF THE SMALE HORSESHOE INDUCES ALL LINK TYPES
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小马蹄铁的三次方涵盖所有链接类型
DOI：
10.1142/s0218216500000542
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发表时间：
2000
影响因子：
0.5
通讯作者：
E. Kin
中科院分区：
文献类型：
--
作者：
E. Kin
设φ：D2→D2是圆盘到自身的保向同胚，Φ= {φt}0≤t≤1是φ0= idD 2且φ1=φ的合痕.则对于φ的周期轨道P的有限并，集合是D2×S1中的一个环。我们说φ诱导所有的链环类型（对于Φ），如果存在D2×S1的同胚h到3-球面S3中的标准嵌入实心环面中，使得S3中的任何链环L可以由φ的周期轨道PL的有限并实现，使得L和等价。我们将表明，Smale马蹄铁和它的第二权力不诱导所有的链接类型，但它的第三权力诱导所有的链接类型。
Let φ:D2→D2 be an orientation preserving homeomorphism of the disk into itself, and Φ= {φt}0≤t≤1 an isotopy with φ0=idD2 and φ1=φ. Then for a finite union of periodic orbits P of φ, the set is a link in D2×S1. We say that φ induces all link types (for Φ) if there exists a homeomorphism h of D2×S1 into a standardly embedded solid torus in the 3-sphere S3 such that any link L in S3 can be realized by a finite union of periodic orbits PL of φ so that L and are equivalent. We will show that the Smale horseshoe and its second power do not induce all link types, but its third power does induce all link types.