Stabilizing Four-Torsion in Classical Knot Concordance

Details Stabilizing Four-Torsion in Classical Knot Concordance Stabilizing Four-Torsion in Classical Knot Concordance

2009-07-31

arxiv.org/abs/0908.0005v1

Mathematics

Geometric Topology

Scientific paper

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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