Abstract:The concordance group of knots in S 3 contains a subgroup isomorphic to (Z 2 ) ∞ , each element of which is represented by a knot K with the property that for every n > 0, the n-fold cyclic cover of S 3 branched over K bounds a rational homology ball. This implies that the kernel of the canonical homomorphism from the knot concordance group to the infinite direct sum of rational homology cobordism groups (defined via prime-power branched covers) contains an infinitely generated two-torsion subgroup.
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