2-torsion in the grope and solvable filtrations of knots

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 $n\ge 4$, there are knots generating a ${\mathbb{Z}}_2^{\infty }$ subgroup of $\G_n/\G_{n.5}$. Considering the solvable filtration, our knots generate a ${\mathbb{Z}}_2^{\infty }$ subgroup of $\F_n/\F_{n.5}$ $(n\ge 2)$ 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.

References in corpus (3)

• The structure of the rational concordance group of knots
• Knots, von Neumann signatures, and grope cobordism
• A topological approach to Cheeger-Gromov universal bounds for von Neumann rho-invariants

Cited by in corpus (1)

• Knots having the same Seifert form and primary decomposition of knot concordance