The complete splitting number of a lassoed link
Geometric Topology
2011-01-04 v3
Abstract
In this paper, we define a lassoing on a link, a local addition of a trivial knot to a link. Let K be an s-component link with the Conway polynomial non-zero. Let L be a link which is obtained from K by r-iterated lassoings. The complete splitting number split(L) is greater than or equal to r+s-1, and less than or equal to r+split(K). In particular, we obtain from a knot by r-iterated component-lassoings an algebraically completely splittable link L with split(L)=r. Moreover, we construct a link L whose unlinking number is greater than split(L).
Keywords
Cite
@article{arxiv.1006.5563,
title = {The complete splitting number of a lassoed link},
author = {Ayaka Shimizu},
journal= {arXiv preprint arXiv:1006.5563},
year = {2011}
}
Comments
14 pages, 10 figures