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]
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