Concordance properties of parallel links
Geometric Topology
2011-08-24 v1
Abstract
We investigate the concordance properties of `parallel links' P(K), given by the (2,0) cable of a knot K. We focus on the question: if P(K) is concordant to a split link, is K necessarily slice? We show that if P(K) is smoothly concordant to a split link, then many smooth concordance invariants of K must vanish, including the tau and s-invariants, and suitably normalized d-invariants of surgeries on K. We also investigate the (2,2m) cables P_m(K), and find obstructions to smooth concordance to the sum of the (2,2m) torus link and a split link.
Keywords
Cite
@article{arxiv.1108.4476,
title = {Concordance properties of parallel links},
author = {Daniel Ruberman and Saso Strle},
journal= {arXiv preprint arXiv:1108.4476},
year = {2011}
}
Comments
15 pages; 5 figures