Branched covers and rational homology balls

Abstract

The concordance group of knots in S 3 contains a subgroup isomorphic to .Z 2 / 1 , 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.