Knot Concordance and Higher-Order Blanchfield Duality
Abstract
In 1997, T. Cochran, K. Orr, and P. Teichner defined a filtration {F_n} of the classical knot concordance group C. The filtration is important because of its strong connection to the classification of topological 4-manifolds. Here we introduce new techniques for studying C and use them to prove that, for each natural number n, the abelian group F_n/F_{n.5} has infinite rank. We establish the same result for the corresponding filtration of the smooth concordance group. We also resolve a long-standing question as to whether certain natural families of knots, first considered by Casson-Gordon and Gilmer, contain slice knots.
Keywords
Cite
@article{arxiv.0710.3082,
title = {Knot Concordance and Higher-Order Blanchfield Duality},
author = {Tim D. Cochran and Shelly Harvey and Constance Leidy},
journal= {arXiv preprint arXiv:0710.3082},
year = {2014}
}
Comments
Corrected Figure in Example 8.4, Added Remark 5.11 pointing out an important strengthening of Theorem 5.9 that is needed in a subsequent paper