Stabilizing Four-Torsion in Classical Knot Concordance

Abstract

Let $M_K$ be the 2-fold branched cover of a knot $Kin$S^3$.If$H_1(M_K) = {\bf Z}_3 \oplus {\bf Z}_{3^{2i}} \oplus G$where3doesnotdividetheorderof$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.

References in corpus (1)

• Lens spaces, rational balls and the ribbon conjecture