Generalized crossing changes in satellite knots

Cheryl Balm

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arXiv · 1210.0885

Generalized crossing changes in satellite knots

Cheryl Balm

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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.

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BibTeX RIS

Cheryl Balm. 2012-10-02. Generalized crossing changes in satellite knots. https://arxiv.org/abs/1210.0885

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