A characterization of the disc
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Th. Friedrich (1974)
Colloquium Mathematicae
Pierre A. Vuillermot (1984)
Mathematische Annalen
Alexis Bonnet (1993)
Manuscripta mathematica
François Laudenbach (2014)
Annales de la faculté des sciences de Toulouse Mathématiques
Heegaard splittings and Heegaard diagrams of a closed 3-manifold are translated into the language of Morse functions with Morse-Smale pseudo-gradients defined on . We make use in a very simple setting of techniques which Jean Cerf developed for solving a famous pseudo-isotopy problem. In passing, we show how to cancel the supernumerary local extrema in a generic path of functions when . The main tool that we introduce is an elementary swallow tail lemma which could be useful elsewhere.
Forman, Robin (2002)
Séminaire Lotharingien de Combinatoire [electronic only]
Alan Weinstein (1978)
Mathematische Zeitschrift
Hutchings, Michael, Lee, Yi-Jen (1999)
Geometry & Topology
Michel Demazure (1973/1974)
Séminaire Bourbaki
Wolfgang Ziller (1976/1977)
Mathematische Zeitschrift
Cornel Pintea (1997)
Annales Polonici Mathematici
We prove that the topological φ-category of a pair (M,N) of topological manifolds is infinite if the algebraic φ-category of the pair of fundamental groups (π₁(M),π₁(N)) is infinite. Some immediate consequences of this fact are also pointed out.
Schütz, D. (2002)
Algebraic & Geometric Topology
R. E. Greene, K. Shiohama (1981)
Annales scientifiques de l'École Normale Supérieure
John R. Klein (1991)
Manuscripta mathematica
Dieter Puppe, Mónica Clapp (1991)
Journal für die reine und angewandte Mathematik
Matthew Grayson, Charles Pugh (1993)
Publications Mathématiques de l'IHÉS
Ţopan, Liana (2003)
Balkan Journal of Geometry and its Applications (BJGA)
E.N. Dancer (1984)
Journal für die reine und angewandte Mathematik
Roberto Pignoni (1979)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Eberhard Teufel (1981)
Mathematische Annalen
Mathias Peternell (1983)
Mathematische Annalen
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