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arXiv:1808.02923math.GT

The Conway knot is not slice

Lisa Piccirillo

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Abstract

A knot is said to be slice if it bounds a smooth properly embedded disk in the 4-ball. We demonstrate that the Conway knot, 11n34 in the Rolfsen tables, is not slice. This completes the classification of slice knots under 13 crossings, and gives the first example of a non-slice knot which is both topologically slice and a positive mutant of a slice knot.

arXiv comments
9 pages, 4 figures (one of which is large), 1 table
Journal reference
DOI
Subjects
math.GTGeometric Topology

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  1. Graduate Student Solves Decades-Old Conway Knot Problem 1 comment

    • Link to paper: https://arxiv.org/abs/1808.02923 I have not read the paper, but I have skimmed it briefly, and it looks pretty exciting. This isn't a case of "here's a new invariant, and, oh, BTW, it works to show the Conway knot isn't slice." It's an actual new technique. And…

      pmiller2View on HNParent context

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