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November 2017 Circle-Valued Morse Theory for Frame Spun Knots and Surface-Links
Hisaaki Endo, Andrei Pajitnov
Michigan Math. J. 66(4): 813-830 (November 2017). DOI: 10.1307/mmj/1508810816

Abstract

Let NkSk+2 be a closed oriented submanifold. Denote its complement by C(N)=Sk+2N. Denote by ξH1(C(N)) the class dual to N. The Morse–Novikov number of C(N) is by definition the minimal possible number of critical points of a regular Morse map C(N)S1 belonging to ξ. In the first part of this paper, we study the case where N is the twist frame spun knot associated with an m-knot K. We obtain a formula that relates the Morse–Novikov numbers of N and K 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

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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

Information

Received: 20 June 2016; Revised: 2 May 2017; Published: November 2017
First available in Project Euclid: 24 October 2017

zbMATH: 06822187
MathSciNet: MR3720325
Digital Object Identifier: 10.1307/mmj/1508810816

Subjects:
Primary: 57Q45, 57R35, 57R45, 57R70

Rights: Copyright © 2017 The University of Michigan

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Vol.66 • No. 4 • November 2017
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