Pseudo-slice knots

Details Pseudo-slice knots Pseudo-slice knots

2000-07-14

arxiv.org/abs/math/0007088v1

Proceedings AMS 130 (2002), 1551-1555 (title: New examples of non-slice, algebraically slice knots).

Mathematics

Geometric Topology

Scientific paper

For n >1, if the Seifert form of a knotted 2n-1 sphere K in S^{2n+1} has a metabolizer, then the knot is slice. Casson and Gordon proved that this is false in dimension three (n = 1). However, in the three dimensional case it is true that if the metabolizer has a basis represented by a strongly slice link then K is slice. The question has been asked as to whether it is sufficient that each basis element is represented by a slice knot to assure that K is slice. For genus one knots this is of course true; here we present a genus two counterexample.

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