Khovanov homology detects the trefoils

Vendredi 8 décembre 14:00-15:00 - Steven Sivek - Imperial College London

Résumé : Khovanov homology assigns to each knot in S3 a bigraded abelian group whose graded Euler characteristic is the Jones polynomial. While it is not known whether the Jones polynomial detects the unknot, Kronheimer and Mrowka proved in 2010 that the Khovanov homology of K has rank 1 if and only if K is the unknot. Building on their work, I will outline a proof that Khovanov homology also detects the left and right handed trefoils, with an emphasis on the role played by contact geometry in this setting. This is joint work with John Baldwin.

Lieu : Université de Nantes, Laboratoire de Mathématiques

Khovanov homology detects the trefoils  Version PDF