The third symmetric potency of the circle and the Barnette sphere
Geometric Topology
2017-09-20 v2 Algebraic Topology
Combinatorics
Abstract
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.
Keywords
Cite
@article{arxiv.1709.02573,
title = {The third symmetric potency of the circle and the Barnette sphere},
author = {Yuki Nakandakari and Shuichi Tsukuda},
journal= {arXiv preprint arXiv:1709.02573},
year = {2017}
}
Comments
7 pages, fixed some typos, corrected wording