On smoothly superslice knots
Daniel Ruberman
TL;DR
This paper constructs smoothly slice knots with Alexander polynomial 1 that are not smoothly superslice, answering a question about the relationship between sliceness and supersliceness in knot theory.
Contribution
It provides explicit examples of smoothly slice knots that are not superslice, clarifying the distinction between these properties in the smooth category.
Findings
Existence of smoothly slice knots with Alexander polynomial 1 that are not superslice
Answer to Livingston-Meier question about superslice knots
Examples of doubly slice knots not being superslice
Abstract
A knot K in the 3-sphere is superslice if there is a slice disk D in the 4-ball such that the double of D along K is the unknotted 2-sphere S in . Answering a question of Livingston-Meier, we find smoothly slice (in fact doubly slice) knots in the 3-sphere with Alexander polynomial equal to 1 that are not smoothly superslice.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Connective tissue disorders research