A note on 0-bipolar knots of concordance order two

Abstract

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