Filtration of the Classical Knot Concordance Group and Casson-gordon Invariants
نویسنده
چکیده
It is known that if any prime power branched cyclic cover of a knot in S is a homology sphere, then the knot has vanishing Casson-Gordon invariants. We construct infinitely many examples of (topologically) non-slice knots in S 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.
منابع مشابه
2 2 A ug 1 99 9 KNOT CONCORDANCE , WHITNEY TOWERS AND L 2 - SIGNATURES TIM
We construct many examples of non-slice knots in 3-space that cannot be distinguished from slice knots by previously known invariants. Using Whitney towers in place of embedded disks, we define a geometric filtration of the 3-dimensional topological knot concordance group. As special cases of Whitney towers of height less than four, the bottom part of the filtration exhibits all classical conco...
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