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Knots and 4-manifolds. (English) Zbl 1481.57013

Summary: These notes are based on the lectures given by the author during Winter Braids IX in Reims in March 2019. We discuss slice knots and why they are interesting, as well as some ways to decide if a given knot is or is not slice. We describe various methods for drawing diagrams of double branched covers of knots in the 3-sphere and surfaces in the 4-ball, and how these can be useful to decide if an alternating knot is slice. We include a description of the computer search for slice alternating knots due to the author and Frank Swenton.

MSC:

57K10 Knot theory
57K40 General topology of 4-manifolds
57-02 Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes

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References:

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