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Showing 1 to 4 of 4 for “"Prime knots"”.
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Khovanov Homology & Uniqueness of Surfaces in the 4-ball
… the 4-ball. We exemplify an infinite family of prime knots that bound an arbitrarily-large number of smoothly-distinct slice disks by distinguishing the maps they induce on Khovanov homology. Similar techniques produce an infinite family of knots that each bound a pair of exotic surfaces of …
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A new structure on Khovanov's homology
… [1] [2] computed this invariant for the prime knots of up to 11 crossings. From the data, Bar-Natan, Garoufalidis, and Khovanov formulated two conjectures on the value of the Khovanov invariant of an alternating knot [1][4]. We prove those conjectures by constructing a new map on …
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On Nullification of Knots and Links
… of a type of local crossing change on oriented knots and links called nullification.</p> <p>One can define a distance between types of knots and links based on the minimum number of nullification moves necessary to change one to the other. Nullification distances form a class of isotopy …