Circle-valued Morse theory for frame spun knots and surface-links
| Autor: | Hisaaki Endo, Andrei Pajitnov |
|---|---|
| Přispěvatelé: | Tokyo Institute of Technology [Tokyo] (TITECH), Laboratoire de Mathématiques Jean Leray (LMJL), Centre National de la Recherche Scientifique (CNRS)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN) |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
General Mathematics
Computation 57Q45 57R35 57R70 57R45 Morse code 01 natural sciences law.invention Combinatorics Mathematics - Geometric Topology Knot (unit) 57R70 law 0103 physical sciences FOS: Mathematics Algebraic Topology (math.AT) 57R35 Mathematics - Algebraic Topology 0101 mathematics Twist [MATH]Mathematics [math] Mathematics::Symplectic Geometry Circle-valued Morse theory ComputingMilieux_MISCELLANEOUS Mathematics 010102 general mathematics Geometric Topology (math.GT) 16. Peace & justice Submanifold Mathematics::Geometric Topology Cohomology 57Q45 010307 mathematical physics 57R45 |
| Zdroj: | The Michigan Mathematical Journal The Michigan Mathematical Journal, Michigan Mathematical Journal, 2017, 66 (4), pp.813-830. ⟨10.1307/mmj/1508810816⟩ Michigan Math. J. 66, iss. 4 (2017), 813-830 |
| ISSN: | 0026-2285 |
| DOI: | 10.1307/mmj/1508810816⟩ |
| Popis: | Let N be a closed oriented k-dimensional submanifold of the (k+2)-dimensional sphere; denote its complement by C(N). Denote by x the 1-dimensional cohomology class in C(N), 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 f from C(N) to a circle, such that f belongs to x. In the first part of this paper we study the case when N is the twist frame spun knot associated to an m-knot K. We obtain a formula which 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. 13 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|