2-torsion in the grope and solvable filtrations of knots

Hye Jin Jang

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arXiv · 1502.04436

2-torsion in the grope and solvable filtrations of knots

Hye Jin Jang

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Abstract

We study knots of order 2 in the grope filtration $\{\G_h\}$ and the solvable filtration $\{\F_h\}$ of the knot concordance group. We show that, for any integer $n\ge4$, 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 $\F_n/\F_{n.5}$ $(n\ge2)$ 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.

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BibTeX RIS

Hye Jin Jang. 2015-02-16. 2-torsion in the grope and solvable filtrations of knots. https://arxiv.org/abs/1502.04436

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