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Cascade Topology Seminar


Prof. Abigail Thompson

Department of Mathematics

One Shields Ave

University of California

Davis, CA 95616 USA 


Title: Generalized Width for Knots in the 3-Sphere

Abstract: This is joint work with Joel Hass and J. Hyam Rubinstein
. A knot K in the 3-sphere is in thin position if it is positioned efficiently with respect to a foliation of the 3-sphere minus 2 points by 2-speres. We generalize this to multiple-parameter families of 2-spheres (or planes, whichever is handy), and show that the generalizations enjoy some useful properties. In particular we show that the generalization to a 2-parameter family yields a proper knot invariant, and ask whether the same is true for higher parameters.


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