Departmental Bulletin Paper ON THE MORSE-NOVIKOV NUMBER FOR 2-KNOTS

Endo, Hisaaki  ,  Pajitnov, Andrei

54 ( 4 )  , pp.723 - 734 , 2017-10 , Osaka University and Osaka City University, Departments of Mathematics
ISSN:00306126
NCID:AA00765910
Description
Let K ⊂ S⁴ be a 2-knot. The Morse-Novikov number ΜΝ(K) is the minimal possible number of critical points of a Morse map S⁴ ∖ K → S¹1 belonging to the canonical class in H¹(S⁴∖ K). We prove that for a classical knot K ⊂ S³the Morse-Novikov number of the spun knot S(K) is ≼ 2ΜΝ(K). This enables us to computeΜΝ(S(K)) for every classical knot K with tunnel number 1
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