Generalized crossing changes in satellite knots
Geometric Topology
2013-03-20 v3
Abstract
We show that if K is a satellite knot which admits a generalized cosmetic crossing change of order q with |q| \geq 6, then K admits a pattern knot with a generalized cosmetic crossing change of the same order. As a consequence of this, we find that any prime satellite knot which admits a pattern knot that is fibered cannot admit a generalized cosmetic crossing changes of order q with |q| \geq 6. We also show that if there is any knot admitting a generalized cosmetic crossing change of order q with |q| \geq 6, then there must be such a knot which is hyperbolic.
Cite
@article{arxiv.1210.0885,
title = {Generalized crossing changes in satellite knots},
author = {Cheryl Balm},
journal= {arXiv preprint arXiv:1210.0885},
year = {2013}
}
Comments
13 pages, 4 figures, a correction was made on page 12