Pseudo-slice knots
几何拓扑
2007-05-23 v1
摘要
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.
引用
@article{arxiv.math/0007088,
title = {Pseudo-slice knots},
author = {Charles Livingston},
journal= {arXiv preprint arXiv:math/0007088},
year = {2007}
}