Stabilizing Four-Torsion in Classical Knot Concordance

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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