2017/09/08 by Yuki Nakandakari, Nakandakari, Yuki, Shuichi Tsukuda +1
Mathematics · #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals #math.AT #math.CO #math.GT
paper · pdf · doi:10.48550/arxiv.1709.02573
7 pages, fixed some typos, corrected wording
openalex publication_date 2017/09/08 · arxiv created 2017/09/19 · arxiv updated 2017/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give an elementary (not cut just paste) proof of results of Bott and Shchepin: the space of non-empty subsets of a circle of cardinality at most 3, which is called the third symmetric potency of the circle, is homeomorphic to a 3-sphere and the inclusion of the space of one element subsets is a trefoil knot. Moreover, we give an explicit simplicial decomposition of the third symmetric potency of the circle which is isomorphic to the Barnette sphere.