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Generalized crossing changes in satellite knots
by
Cheryl Balm
Michigan State University
We will show that if K is a satellite knot which admits a generalized cosmetic crossing change of order q with |q| ≥ 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 change of order q with |q| ≥ 6. We also show that if there is any knot admitting a generalized cosmetic crossing change of order q with |q| ≥ 6, then there must be such a knot which is hyperbolic.
Date received: October 23, 2012
Copyright © 2012 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbfw-08.