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Two-torsion in the grope and solvable filtrations of knots

Hye Jin Jang

Department of Mathematics, POSTECH, Pohang, 790–784, Republic of Korea

E-mail Address: hyejin.jang1986@gmail.com

https://doi.org/10.1142/S0129167X17500239Cited by:3 (Source: Crossref)

Abstract

We study knots of order $2$ $2$ in the grope filtration ${𝒢_{h}}$ and the solvable filtration ${ℱ_{h}}$ of the knot concordance group. We show that, for any integer $n \geq 4$ , there are knots generating a $ℤ_{2}^{\infty}$ subgroup of $𝒢_{n} / 𝒢_{n . 5}$ . Considering the solvable filtration, our knots generate a $ℤ_{2}^{\infty}$ subgroup of $ℱ_{n} / ℱ_{n . 5}$ $(n \geq 2)$ distinct from the subgroup generated by the previously known $2$ -torsion knots of Cochran, Harvey, and Leidy. We also present a result on the $2$ -torsion part in the Cochran, Harvey, and Leidy’s primary decomposition of the solvable filtration.

Keywords:

AMSC: 57M25, 20J

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