English

A note on 0-bipolar knots of concordance order two

Geometric Topology 2017-12-29 v1

Abstract

Let T\mathcal{T} be the group of smooth concordance classes of topologically slice knots, and {0}Tn+1TnT0T\{0\}\subset\cdots\subset \mathcal{T}_{n+1}\subset\mathcal{T}_{n}\subset \cdots\subset \mathcal{T}_{0}\subset \mathcal{T} be the bipolar filtration. In this paper, we show that a proper collection of the knots employed by Hedden, Kim, and Livingston to prove Z2<T\mathbb{Z}_2^{\infty} < \mathcal{T} can be used to see Z2<T0/T1\mathbb{Z}_2^{\infty} < \mathcal{T}_0/\mathcal{T}_1.

Keywords

Cite

@article{arxiv.1712.09622,
  title  = {A note on 0-bipolar knots of concordance order two},
  author = {Wenzhao Chen},
  journal= {arXiv preprint arXiv:1712.09622},
  year   = {2017}
}