Filtration of the classical knot concordance group and Casson-Gordon invariants

Abstract

It is known that if any prime power branched cyclic cover of a knot in the 3-sphere is a homology sphere, then the knot has vanishing Casson-Gordon invariants. We construct infinitely many examples of (topologically) non-slice knots in the 3-sphere whose prime power branched cyclic covers are homology spheres. We show that these knots generate an infinite rank subgroup of F_(1.0)/F_(1.5) for which Casson-Gordon invariants vanish in Cochran-Orr-Teichner's filtration of the classical knot concordance group . As a corollary, it follows that Casson-Gordon invariants are not a complete set of obstructions to a second layer of Whitney disks.