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An Elementary Proof That the Third Finite Subset Space of the Circle is the 3-Sphere
The American Mathematical Monthly ( IF 0.4 ) Pub Date : 2020-10-20 , DOI: 10.1080/00029890.2020.1811002
Yuki Nakandakari 1 , Shuichi Tsukuda 2
Affiliation  

Abstract We give an elementary cut-and-paste proof of results of Bott and Shchepin: the third finite subset space of the circle is homeomorphic to the 3-sphere and the inclusion of the first finite subset space in it is a trefoil knot. Moreover, we give an explicit simplicial decomposition of the space which is isomorphic to the Barnette sphere.

中文翻译:

圆的第三个有限子集空间是三球体的初等证明

摘要 我们给出了 Bott 和 Shchepin 结果的基本剪切和粘贴证明:圆的第三个有限子集空间同胚于 3 球体,其中包含的第一个有限子集空间是一个三叶结。此外,我们给出了与 Barnette 球同构的空间的显式单纯分解。
更新日期:2020-10-20
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