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Yohan Mandin-Hublé

Topological sliceness of knots with trivial Alexander polynomial
Vendredi, 8 Avril, 2022 - 10:30
Résumé : 

We will give a proof, due to Garoufalidis and Teichner, of the following 
result of Freedman : knots with trivial Alexander polynomial are 
topologically slice, which means that they bound an embedded locally 
flat two dimensional disk in the four-ball. The Alexander polynomial is 
a well-understood and easy-to-compute invariant of knots, whose 
definition will be recalled. The proof makes use of a more fundamental 
result of Freedman, the disk embedding theorem. We will state this 
theorem and derive the former as one of its corollaries by some 
elementary topological considerations.

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