Cosmetic crossings and Seifert matrices
Geometric Topology
2013-06-24 v2
Abstract
We study cosmetic crossings in knots of genus one and obtain obstructions to such crossings in terms of knot invariants determined by Seifert matrices. In particular, we prove that for genus one knots the Alexander polynomial and the homology of the double cover branching over the knot provide obstructions to cosmetic crossings. As an application we prove the nugatory crossing conjecture for twisted Whitehead doubles of non-cable knots. We also verify the conjecture for several families of pretzel knots and all genus one knots with up to 12 crossings.
Keywords
Cite
@article{arxiv.1108.3102,
title = {Cosmetic crossings and Seifert matrices},
author = {Cheryl Balm and Stefan Friedl and Efstratia Kalfagianni and Mark Powell},
journal= {arXiv preprint arXiv:1108.3102},
year = {2013}
}
Comments
16 pages, 5 Figures. Minor revisions. This version will appear in Communications in Analysis and Geometry. This paper subsumes the results of arXiv:1107.2034