Abstract
Let be a closed oriented submanifold. Denote its complement by . Denote by the class dual to . The Morse–Novikov number of is by definition the minimal possible number of critical points of a regular Morse map belonging to . In the first part of this paper, we study the case where is the twist frame spun knot associated with an -knot . We obtain a formula that relates the Morse–Novikov numbers of and and generalizes the classical results of D. Roseman and E. C. Zeeman about fibrations of spun knots. In the second part, we apply the obtained results to the computation of Morse–Novikov numbers of surface-links in 4-sphere.
Citation
Hisaaki Endo. Andrei Pajitnov. "Circle-Valued Morse Theory for Frame Spun Knots and Surface-Links." Michigan Math. J. 66 (4) 813 - 830, November 2017. https://doi.org/10.1307/mmj/1508810816
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