Stabilizing Four-Torsion in Classical Knot Concordance

Charles Livingston; Swatee Naik

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arXiv · 0908.0005

Stabilizing Four-Torsion in Classical Knot Concordance

Charles Livingston·Swatee Naik

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Abstract

Let $M_K$ be the 2-fold branched cover of a knot $K in $S^3$. If $H_1(M_K) = {\bf Z}_3 \oplus {\bf Z}_{3^{2i}} \oplus G$ where 3 does not divide the order of $G$ then $K$ is not of order 4 in the concordance group. This obstruction detects infinite new families of knots that represent elements of order 4 in the algebraic concordance group that are not of order 4 in concordance.

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Charles Livingston, Swatee Naik. 2009-07-31. Stabilizing Four-Torsion in Classical Knot Concordance. https://arxiv.org/abs/0908.0005

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