I'm very curious to learn how Piccirilo proved that the Conway Knot is not slice. What should I study to understand her paper in details?
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$\begingroup$ Give a little more details, for example the references to this paper. Besides, I am not sure to understand what you mean by "Conway Knot is not slice".... Is it the correct way to say it in English (which is not my native language) ? $\endgroup$– Jean MarieMar 7, 2022 at 19:38
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2$\begingroup$ Yes, that's the correct way. In knot theory, "slice" is an adjective. $\endgroup$– Robert ShoreMar 7, 2022 at 19:50
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$\begingroup$ another way might be (better?) "is not a slice knot" $\endgroup$– ypercubeᵀᴹMar 8, 2022 at 19:10
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1$\begingroup$ @ypercubeᵀᴹ You can say that, though knot theorists usually say "this knot is (not) slice" when its the property and "slice knots" when it's the class. "Every ribbon knot is slice" shows the convention, which applies to "ribbon" as well. $\endgroup$– Kyle MillerMar 8, 2022 at 21:31
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1$\begingroup$ @JeanMarie Here's the paper: arxiv.org/abs/1808.02923 (note: "the Conway knot is not slice" is the title of the paper.) $\endgroup$– Kyle MillerMar 8, 2022 at 21:34
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1 Answer
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Quick answer for what to study:
- Rolfsen "Knots and Links" for knot theory; be sure to pay attention to things about surgeries.
- Gompf and Stipsicz "4-manifolds and the Kirby calculus" for more details about that.
- Probably Ozvath, Stipsicz, Szabo "Grid homology for knots and links" for Floer homology. (I don't know too much about this part of knot theory, and there might be better references.)
- Bar-Natan's papers about Khovanov homology.
It's worth looking through the references of Piccirillo's paper, and references of references, but this should at least get you started.
answered Mar 8, 2022 at 21:40