Generalized crossing changes in satellite knots
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- by Cheryl Jaeger Balm
- Proc. Amer. Math. Soc. 143 (2015), 447-458
- DOI: https://doi.org/10.1090/S0002-9939-2014-12235-0
- Published electronically: August 18, 2014
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Abstract:
We show that if $K$ is a satellite knot in the 3-sphere $S^3$ 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 in $S^3$ which admits a torus knot as a pattern cannot admit a generalized cosmetic crossing change of order $q$ with $|q| \geq 6$. We also show that if there is any knot in $S^3$ admitting a generalized cosmetic crossing change of order $q$ with $|q| \geq 6$, then there must be such a knot which is hyperbolic.References
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Bibliographic Information
- Cheryl Jaeger Balm
- Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
- Email: balmcher@math.msu.edu
- Received by editor(s): October 23, 2012
- Received by editor(s) in revised form: March 14, 2013, and March 19, 2013
- Published electronically: August 18, 2014
- Additional Notes: This research was supported by NSF grant DMS-1105843
- Communicated by: Daniel Ruberman
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 143 (2015), 447-458
- MSC (2010): Primary 57M27
- DOI: https://doi.org/10.1090/S0002-9939-2014-12235-0
- MathSciNet review: 3272768