On the tunnel number and the Morse-Novikov number of knots

Abstract

We prove that the Morse-Novikov number of a link L in a 3-sphere is less than or equal to twice the tunnel number of L.

8 pages, revised and extended

References in corpus (3)

• Twisted Alexander polynomials detect the unknot
• Constructions of Morse maps for knots and links, and upper bounds on the Morse-Novikov number
• Murasugi sums of Morse maps to the circle, Morse-Novikov numbers, and free genus of knots

Cited by in corpus (3)

• Dislocations and Fibrations: The Topological Structure of Knotted Smectic Defects
• The Morse-Novikov number of knots under connected sum and cabling
• Circular handle decompositions of free genus one knots