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

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

2002-07-24

arxiv.org/abs/math/0207221v1

Mathematics

Geometric Topology

13 pages, 5 figures

Scientific paper

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.

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