ON THE MORSE-NOVIKOV NUMBER FOR 2-KNOTS

Hisaaki Endo (1) , Andrei Pajitnov (2)

1 TITECH - Tokyo Institute of Technology [Tokyo]
2 LMJL - Laboratoire de Mathématiques Jean Leray

Let K ⊂ S4 be a 2-knot. The Morse-Novikov number M N (K) is the minimal possible number of critical points of a Morse mapS4\K→S1belonging to the canonical class inH1(S4\K). We prove that for a classical knotK⊂S3the Morse-Novikov number of the spunknotS(K)is< 2 M N(K). This enables us to compute M N (S(K)) for every classical knot K with tunnel number 1

Domaines: Mathématiques [math]

Hisaaki Endo, Andrei Pajitnov. ON THE MORSE-NOVIKOV NUMBER FOR 2-KNOTS. Osaka Journal of Mathematics, 2017, 54, pp.723 - 734. ⟨hal-02383614⟩