Signature and concordance of positive knots

Sebastian Baader (1) , Pierre Dehornoy (2) , Livio Liechti (3)

1 Mathematisches Institut [Bern]
2 IF - Institut Fourier
3 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche

We derive a linear estimate of the signature of positive knots, in terms of their genus. As an application, we show that every knot concordance class contains at most finitely many positive knots.

Domaines: Topologie géométrique [math.GT]

Sebastian Baader, Pierre Dehornoy, Livio Liechti. Signature and concordance of positive knots. Bulletin of the London Mathematical Society, 2018, 50 (1), pp.166-173. ⟨10.1112/blms.12124⟩. ⟨hal-02320331⟩