A note on 0-bipolar knots of concordance order two

Chen, Wenzhao

doi:10.1090/proc/14315

A note on $0$-bipolar knots of concordance order two
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by Wenzhao Chen

Proc. Amer. Math. Soc. 147 (2019), 1773-1780

DOI: https://doi.org/10.1090/proc/14315

Published electronically: December 12, 2018

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Abstract:

Let $\mathcal {T}$ be the group of smooth concordance classes of topologically slice knots, and let $\{0\}\subset \cdots \subset \mathcal {T}_{n+1}\subset \mathcal {T}_{n}\subset \cdots \subset \mathcal {T}_{0}\subset \mathcal {T}$ be the bipolar filtration. Hedden, Kim, and Livingston showed that $\mathcal {T}$ contains a subgroup isomorphic to $\mathbb {Z}_2^\infty$. In this paper, we show that a subset of the set of knots constructed by Hedden, Kim, and Livingston generates a subgroup isomorphic to $\mathbb {Z}_2^{\infty }$ in $\mathcal {T}_0/\mathcal {T}_1$.

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